ME1 no doubt had its problems, but it was easily the most cohesively written of the three. Its biggest problems can be solved with a bit of exposition, whereas ME2 and 3's...can't.
That's the cruft of it--we don't know how long he was under investigation. I've said it before, but, along with the characters jumping to wild conclusions on information they shouldn't have ("Saren must have used the beacon! He wants to launch an attack on Earth! Reapers! REAPERS! REAPERS!"), time scales are amongst ME1's biggest narrative flaws. Shepard is out for 18 hours. In that time, the Normandy is *just* approaching the Citadel, where Anderson and Shepard are intent on proving Saren's wrongdoing to the Council, yet soon thereafter, Garrus will appear, claiming that he couldn't find anything in his investigation. What? Ignoring that it's kind of silly that he was tasked by the Council to look into a specTRe's activities, yet was never given access to restricted files, what sort of formal criminal inquiry is less than a day? And why was Saren being investigated if the Council maintains that he was innocent of any wrongdoing? Then there's Tali and Dr Michel, who claim to have met what would have to be a significant time ago (days or weeks, maybe), yet there is no report of geth activity before Eden Prime.
If I were to fix these (and these are just rough ideas):
- The Council's protecting Saren would be an actual plot point revealed as the story progresses: The Council structure is losing legitimacy amongst the alien home worlds. There are centralist/supremacist movements on Sur'Kesh, Palavan, and Thessia (could tie into the biotic supremacist matriarch that Cerberus kidnapped and medicated in the extended universe--which would also lend legitimacy to Cerberus' pro-human tendencies--Matriarch Dilinaga's writings, and the eventual Thessian beacon reveal), who are locked in a clandestine arms race (the secrets Liara talks about in LotSB could be major plot points because of this). As specTres are the right arm of the Council, they are resented by the home world governments. The Council fears that implicating its top agent may further shift the balance of power out of their hands and into factions--possibly weakening the galaxy against the allied power of the Terminus Systems.
- Citadel space and the Terminus Systems have been at war several times throughout history, all of them bloody and ending at tremendous cost. This lends urgency to Shepard's operations in ME1/2, makes allying with Aria more significant, and makes the Council's inaction/concerns about Shepard's mercenary outfit in ME2 more logical.
- Saren has been under "investigation" for some time: the Council has not released restricted files to Garrus, despite the fact they know he has been diverting large amounts of Council/specTRe money and resources to undisclosed places (Shepard will learn this from Barla Vonn, the beginning of a close relationship with the SB that ultimately ends in betrayal, as the SB sends Shepard to the rendezvous where the Normandy is attacked in ME2's intro), and may possibly be responsible for the large number of recent merc/pirate attacks on human merchant, Kowloon-class supply vessels headed for human outskirts colonies (the Terminus is officially responsible for this; all those side missions where Shepard boards vessels become part of plot-relevant investigation). When Saren is finally stripped of specTRe status, they grant Shepard agency as a threefold political gambit: it replaces their lost agent, bolsters their power by garnering the support of another species (the Alliance), and placates the humans whilst not forcing the Council to make any real commitments; the humans are taking care of the problem of their at-risk colonies themselves, and by stripping (or so they think) Saren of access to resources and sending s newbie specTRe after him, they needn't take real action or weaken their position as the central galactic power.
- Saren/Sovereign's end game plan is to excite war between the Council home worlds,
Council loyalists, and the Terminus Systems so as to weaken the galaxy against the reapers: This fact is revealed as the story progresses. Speaking with Wrex, who (canonically) tells Shepard he was once hired by Saren to "raid a ship." This leads (the only location Shepard is given in the beginning is Liara's) Shepard to investigate the increase in merchant ship disappearances, revealed to be Saren's work by way of hiring out PMCs (led by Elanos Haliat) of mercs--including those funded by the embittered Hegemony-- to pose as Terminus factions engaging in acts of war (this ties into the Helena Blake side missions and Nassana Dantius, who Shepard can threaten to blackmail for more information). One of the derelict ship's contents contains strange ExoGeni data caches about drops in Matano (leads to Cerberus subplot) and the "experimental colony," Feros. Cue Feros side mission.
- The Thessian Matriarchs are themselves split into factions: One faction believes that the asari should be the dominant power in the galaxy (by abusing the beacon, again only revealed in ME3), one believes that the asari should remain mediators, and one believes that the asari should take a more active role in galactic politics by revealing the beacon to the galaxy, whose tech could help in preparation for the impending war with the Terminus. Matriarch Benezia belonged to the latter group. As the matriarchs could not reach consensus, the secret of the beacon was kept amongst a small circle of them, whilst each faction amassed a following of commando apostles. Benezia, for her part, suspected Saren's activity could possibly provoke/lead a war against Citadel space using the Terminus alliance (a plan eventually squashed by Shepard's killing Elanos Haliat), and made it her personal mission to dissuade him. For her troubles, she is indoctrinated. All of this (sans the existence of the beacon, as she doesn't know) is revealed by Shiala on Feros, where Shepard receives the cipher. Feros is also the first place Shepard encounters Saren's krogan. They are larger than usual, somewhat crazed, and "off-looking" (courtesy Wrex).
- Shepard doesn't really believe in the Reapers until she receives the cipher on Feros, and Saren/Sovereign was after Liara because of her work on extinction cycles: Liara is the only prothean expert who claims their disappearance as her primary field of focus. Though there are others that study the fall of the prothean empire, she is the only one that espouses the idea of "extinctions," and she is largely disgraced in the scholastic realm because of it. When (pre-Feros) Shepard sceptically asks for proof of her theory, she provides several dig sites across the galaxy, and a few theses. Shepard prefers to investigate the dig sites. (Post or pre-Feros) Liara makes the comment that the beacon would have "destroyed a lesser mind," prompting Shepard to remember Dr Manuel Cayce, and seek him out.
- Dr Cayce has a larger role in the series: Seeking out Dr Cayce, Shepard discovers he has been sent to a sanitorium by his cousin, Dr Warren. At the asylum, Shepard questions case, whose OCD tendencies and paranoia have worsened into delusions and schizophrenic tendencies (or so the doctors think). Dr Cayce, who is forcibly medicated so he can sleep, wakes up in hysteria and engages in ritualistic counting, claiming it and arranging objects in a certain manner keeps "them" from coming through. Shepard realises that Cayce used the beacon (and possibly damaged it). Cayce admits he did use it, though for a shorter time than Shepard did. Somewhat placated by Shepard's promise to stop the reapers from pouring through, he gives her locations of his and Dr Warren's previous research sites (ties into all the the strange prothean artefacts you can stumble upon in ME1). The prothean globe Shepard stumbles upon reacts to the cipher (and Sha'ira's trinket--something later revealed to be a activation key from the Thessian beacon passed down from her matriarch parents), revealing not only the Cro-Magnon memories, but a star map marked with locations. Shepard can interpret it because of the cipher, and along with Liara's dig sites, she pieces together that the pyramids (ex. the one on Chasca) are actually prothean communication hubs, and all once held beacons.
- The data caches found on Feros lead Shepard to mistakenly believe ExoGeni is involved with Saren: Here, the Cerberus subplot begins to unravel. As Shepard destroys Cerberus bases, she progressively realises they are unrelated to Saren. The Cerberus cell, for their part, seeks to use genetic engineering and their research into cybernetics, thorn creepers, and rachni to create super soldiers. To this end, they have captured, experimented upon, and killed several people (along with the attendant accidents, like the release of the rachni; In ME2, it is revealed that the same research Shepard disrupted is what is responsible for her superhuman upgrades). The rachni lead traces back to the genetic modification company, Binary Helix. As per a trade for Cerberus intel, the SB reveals that Saren (and recently, Benezia) had been heavily investing in the company--using Council money, no less. In light of this, Shepard decides to make a corporate inquiry on Noveria.
- On Noveria, things play out as they do in ME1, with the exception that the Mallene Callis side mission can be plot integral. Since the board still doesn't want Shepard getting too close to their investors, though Shepard may help Anoleis or Gianna, she may visit Peak 15, but she may not see the laboratories proper. If Shepard agrees to help Callis with her espionage (lie or not), Callis gives Shepard access codes. If not, Shepard is forced to break into the labs in a stealth-based level. As Peak 15 is in a state of lockdown, when it is discovered that there is an infiltration, the ERCS guards panic and begin to execute the scientists. Paragon points can be netted for saving them, renegade points for continuing with the objective, and so on. Shepard finds data that suggests that Saren has been researching a way to circumvent the genophage (data later revealed to have been repurposed by the Collectors/Harbinger and used to make Grunt), and after being confronted by Alestia Iallis, realises that Benezia is, in fact, near by and so on. Benezia reveals that Saren intends to use the rachni not just for the Mu Relay, but as disposable shock troopers in his Terminus alliance/geth/krogan war machine.
- Benezia's death has serious implications: Because Benezia was a leader in one of the Thessian factions, the balance of power has again shifted, which deeply concerns the Council (and puts Shepard squarely on their sh*tlist, leading to her grounding) as it looks like an aggressive act against the asari centrists (though the opposing faction takes an interest in Shepard, and is responsible for sending out Samara in ME2). The asari councillor chastises Shepard, though it isn't clear what the tension is about until the ME3 beacon reveal. More pressing, however, is the news that Saren is attempting to circumvent the genophage. The Council, who up until this point has been sitting on their arses, decides to send STG to investigate possible facilities Shepard has provided.
- Saren got the Virmire beacon from one of the pyramids: This quest opens up any time after Feros and the sanatorium. Shepard investigates the communications hubs/ruins, the cipher and activation key opening up systems long-thought to be derelict. The Normandy crew finds the largest (and central) pyramid, where Shepard believes may house another working beacon. However, once the ground team lands and enters, it is revealed that Saren has gotten there first (the Virmire beacon was this one), and the party is ambushed by geth. One of the geth shoots a strange device at Shepard, which lodges in Shepard's chest and seriously wounds her. As her squad mates carry her back, they just miss the other geth platforms begin to attack the one responsible (in ME2 this geth is revealed to have been Legion--Shepard's injury was accidental, and his comrades attacking him is how the hole in his chest came to be). Back on the Normandy, the "device" is revealed to be a geth data disk that gives the locations of a geth incursion--the first wave of invasion by Saren's forces (after these side missions, Tali gets/doesn't get her data).
- The crew actually witness the army of krogan on Virmire: After another unsuccessful raid on one of Saren's possible bases, the Council informs Shepard that one of their STG task forces haven't reported in. Virmire continues as scripted, with the small addition of Shepard actually seeing the thousands of mindless, degenerating krogan being bred in a room full of tanks. Depending on how Shepard handles Wrex/Virmire, the salarian centrists are more open to Shepard in ME2.
- Killing the Council or saving them has ramifications in ME2: After two years, not only has security increased on the Citadel, it is under martial law. C-Sec is spreading its influence such that it is more like a galactic army, the central governments are bolder, and the Council's power more unstable (hence why, if saved, they are hesitant to see Shepard, but reinstate her specTRe status anyway, or--if there is a new Council--don't want to see Shep at all). The Terminus merc gangs grow in power and divide into factions of their own (Aria allies with Shep out of mutual benefit); Zaeed acts as a liason. Cerberus is also a faction. Shepard can choose to align with any one of these groups or many, provided their interests don't conflict (win over quarians by helping quarians like Kenn et al, the salarians by having killed Wrex, asari bigwigs send Samara on an investigation, or side with Cerberus, the merc gangs, the Alliance, or the Citadel Council, etc).