Here's what I'd change about either the characters, or the plots in relation to said characters.
Kaidan - He's always been more mild-mannered, calmer, and prone to rational decision making, and I would have that show in ME2 and ME3. Refuse to go with Shepard, but not be so judgmental and pissy about it. Give me a few scenes where we can really have the point hammered home that the Cerberus in ME2 was a front TIM put out for Shepard to see (if anyone thinks this is an invalid point, it's brought up on Priority: Cerberus Headquarters). Make the distrust of Shepard less about "working with Cerberus" and more "Did TIM do anything to you, is he listening in on our conversations or anything, I wouldn't put that past him. I worry for the war effort." Sensible, rational reasons.
I'd also give him a side-mission that lets us explore his character a bit. He has conversations with the Normandy folks (a few more with Tali and Garrus wouldn't hurt, though), but it felt inadequate compared to what everyone else got.
Ashley - I don't mind her letting her hair down, or her jacket on the Normandy, but let her pin her hair back up for a mission, it's just practical, you don't want your hair flying everywhere in a war zone. Give her conversations with the cast about different things. Ashley is spiritual, let her talk with Liara about siari, or Garrus about the spirits. To counterbalance Kaidan talking with Adams, let's have Ashley chat up Dr. Chakwas or Dr. Michel.
I'm okay with Ashley being more hot-headed about Cerberus since it fits her character, but give her an additional reason, something a bit less crazy.
Both Ashley and Kaidan - If they're siding with me unconditionally, they should not talk about possibly regretting their decision, nor should Ash mention Cerberus (Kaidan's "you have a gun on Udina" line is fine). They should say something like "I get what's going on, Shepard" and then move to shoot Udina.
Liara - I'd cut her from the Normandy squad. Seriously, nothing in her entire story justifies her being on that ship. Her ME1 plot relevance is limited to picking out Ilos, her ME2 relevance is nonexistent, and her ME3 importance is mainly being the Shadow Broker, in which she does nothing at all but receive a few messages (and I have Traynor and EDI doing that already. In ME1, I should be able to ignore her. In ME3, once I pick her up on Mars and bring her to the Citadel, she should go to the Crucible, help with it's design. She should give me missions specific to Prothean tech or the Crucible instead of Hackett.
And drop the Shadow Broker aspect. It has zero plotline relevance and only serves to try and make her look good. She's a Prothean scientist, that's all. This would also cut down on her lines, and I'm cool with that. Liara was shoveled onto us as a best friend/lover, and I didn't buy it. I didn't get why I was hugging her, or why she was inviting herself up to my cabin.
Wrex - Wrex is a terrible leader, and made all of the horrible, yet utterly fascinating, moral complexity about the genophage go away. Make his story actually have a more realistic bent to it: He doesn't understand what a krogan population boom means. He might think he does, but he doesn't. Make the hardline clans cause a war after the Reaper invasion, and Wrex has to deal with it. Make a Wrex/No Eve world just as bad as one with Wreav, since that's what would realistically happen: He just can't control that many people, and he thinks that the krogan taking giant chunks of the galaxy is fine anyway, as long as they ask first. Give me a chance to call out Wrex on being such a crappy leader. I either had to betray him or give him a pass, and that aggravated me. Bottom line, treat Wrex as what he is: A well-meaning guy who can't comprehend the full meaning of his choices because he is so jaded about the cure.
Kirrahe - Let me put this awesome salarian on my squad
Jacob - Give me a reason to root for him. Maybe Brynn could have been a former flame he already knew before ME2, and I inspire him to go back to her, and he then becomes a better father.
Jack - Let me get inside her head without needing to get inside her pants. The conversations were likable, but you can do that without romance.
Legion - Let someone on the Citadel DLC at let mention Legion.
EDI - I don't mind her growth arc. I didn't care for the sexbot body, though. She can do that without being a sexbot. Her platonic relationship with Joker was just fine.
Now, as for plot instances...
On Virmire, they had a dummied out version of saving Ashley and Kaidan both, I'd restore it. It fits with the theme of the game: If you want to succeed, you better damn well do everything right and put in some major risk. Or, let me pick the person setting the bomb. I'd just as quickly give the role to Liara.
I'd cut the Lair of the Shadow Broker, or at least cut Liara out of it. Shepard literally had no reason to go along with that mission. He could have handed it off, then went to go recruit Samara or someone. There was no need for him to be there.
I'd add a series of Spectre missions in the third game, that lets us see inside other Spectres. The only ones we got to see were corrupt amoral jerks and Jondum Bau, who had all of one scene. You can put Ashley/Kaidan on those missions too, let us see inside their character head, how they feel about Spectrehood.
During the third game, I saw an overabundance of krogan and asari, the right amount of quarian and drell, some (but not very much of) turian and salarians, and almost nothing at all with the batarians, volus, elcor, and vorcha. There needed to be more balance.