Kai Leng is more ridiculous, yes. He looks like he's come straight out of a comic, his lines are mediocre at best, if I recall well he doesn't carry guns, he's one dimensional and merely a plot device. Some explanation is given about the Thorian. It's supposed to be weird and alien.
"Some explanation is given."
To be clear I don't really care about any of this but a lot of leeway is being given to one game and not the two others.
Why does the Catalyst look like the kid?
The Catalyst establishes a mental link with Shepard, something which has been shown possible multiple times previously, especially in ME1.
Why does Shepard care so much about this damn kid?
He doesn't. The kid is a symbol for all the death and destruction during the series.
Why spend tons of money on resurrecting Shepard when they could have just cloned him/her?
Citadel DLC as well as TIM gives you the answer, but a clone doesn't have any of Shepard's experiences that have turned him into the guy TIM knows can get the job done.
They don't need a "symbol". They need an army. They couldn't even count on his loyalty.
TIM doesn't need Shepard's loyalty to stop the Collectors; he only needs to count on Shepard's willingness to take them on. As for keeping the Collector base, his only miscalculation was Miranda betraying him.
"Why are the Crucible plans so conveniently found in Mars, which has been scouted for decades?"
Because the plot dictates that it needs to be found. It also gives credibility to Shepard's decision to destroy the relay in Arrival, since it's only in the 6 months this gives Liara that she utilizes the Broker network to locate the plans.
The obvious reasons for a lot of things will be "because the plot needed it to happen now" but this doesn't automatically make the story point bad. Why does Shepard survive the beacon in ME1? Magical "Shepard is teh man/woman" reasons to serve the plot. That being said if I were given a do-over I'd have made ME2's plot revolve around obtaining the Crucible plans.
"Why does everyone decide to go along with it, spending a great deal of money and resources, even if nobody knows what it does exactly? It's cheap."
Because everyone agrees that conventional victory is a dead end, and that at bare minimum they know, as Liara says, that it's a device capable of channeling energy into untold amounts of destruction.
"Cerberus started out as a rogue scientific/martial organization. How did it become an empire in such little time? Why do the same few dumb characters hold all the power? (Most are portrayed as dumb. Loghain, Eamon, Anora from DAO are fine examples of well written scheming people. They don't sound like babbling idiots.)"
We know this is because it's only after ME1 that BW decided to make Cerberus important, but it's easy to write this off as tactical misinformation on Cerberus' part; misrepresent their strength so that they don't draw the attention of people like the Alliance. As for dumb characters, of whom do you speak? What about TIM's plan is dumb, especially since he turned out to be right all along?
"What's the point of making Udina indoctrinated?"
Was he? I thought he was a Cerberus insider. Was it confirmed he was indoctrinated? If he was, it was to reinforce the danger of indoctrination, something which has been a central plot point the entire series, and which Javik identifies as a primary reason for their defeat (choosing to give up planets only for the inhabitants to be used to replenish Reaper troops).
"Why does Shepard keep on ranting about Earth? The whole galaxy is at stake."
Shepard cares about the home world of his species, oh no.
Some of your concerns are actually quite nitpicky and conditional, and for every one you come up with from ME3 I can give you one from ME1. How about the fact that if some lazy dock worker hadn't slept behind a pile of boxes (miraculously undetected by the droves of geth running around) Saren isn't identified, Shepard has no reason to find Tali, and Sovereign's plan succeeds? All hail the true hero, Mr. Procrastinating Dock Worker!