Mass Effect 2: Let's see if I can do this from memory.
1: How did the collectors find the Normandy? I know they're hitting colonies and ships and whatnot, but they freakin' ambush the Normandy from FTL.
2: If Joker is as fragile as he claims, how did he not break something when Shepard was yanking him up out of the chair?
3: How did Shepard's body not burn up on reentry? Okay, so technically the armor could be rated for reentry, but this is something we've never heard before or since, and it also leaves us with another immediate plothole.
4: How can you make a cyberzombie Shepard if you didn't recover the head!? If Shepard's armor was rated for reentry, and they did find the corpsicle that way, why the hell is Shepard's helmet still at the crash site!?
5: Why is Shepard's helmet still at the crash site!? If the site was looted for Shepard's body then it should have been, you know looted. We're told this was by Shadow Broker agents who aren't the most subtle of individuals, and generally not inclined to leave boxes of Ezo around for Shepard to snarf up later.
6: (...and finally moving on past the opening credits.) "How does Shepard know how to use the disposable thermal clips?" has been brought up before, so has "What happened to the reusable heat-syncs?" so here's a fresh one: Ejecting a heat-sync off of any electronic component isn't a way to make it cool down faster, it's a way to make it crack. So how is this any more beneficial than simply letting the heat-sync cool off naturally? ...maybe it's a geth plot...
7: Why did Wilson try to kill you? This would make perfect sense if the collectors used intermediaries with any frequency and had a way to find out Wilson was pissed off at his job.
8: Why is Wilson pissed off at his job? The only hint we get is that he'd like to see a little more cash. I'm sure we've all been there, a job that isn't quite worth the pay, but most of us don't immediately decide to go into the security office and start gunning people down by remote control.
9: In an audio log Miranda observes that Shepard needs to be the same man/woman/escaped football captain that he/she/it was before. Which is all well and good until you realize the game just had you rebuild your character basically from scratch 10 minutes earlier. Now, I understand that the re-spec retroactively changed who you were in the previous game, but it's still an incredibly stupid comment to make, and it isn't the only one. None of this explains where (potentially) 55 of your levels just went.
10: Miranda says Shepard needs to have the same morals... er, what? This leads into a thing, in Mass Effect: Paragon was roughly Jean-luc Picard while Renegade was roughly Jack Bauer on the way to the bathroom. But in ME2 that's not quite the same thing, Paragon is now more in line with Jeffery Sinclair (good to a fault, but dumb as a brick, while pretending to be cunning), while Renegade has changed to the goddamn Joker.
11: Unless it was Miranda (and not Wilson) was secretly behind the attempt to assassinate Shepard, why did she execute him without even trying to decipher his motives? When asked, she responds that, he was too dangerous to keep around. Oh yeah? Dangerous to whom?
12: How can you adequately judge someone's mental state by asking three questions? (Or worse yet, two if you didn't import a save?).
13: How did Cerberus afford all these new toys? In the first game you run across one Cerberus "space station", and that's it, in point of fact it's a re-purposed collection of freighters which has been converted into a kind of depot.
14: Why did Cerberus start custom building stations? Big Stations, with distinctive architecture, and a Corporate friendly Cerberus Logo on everything? You see, in the first game they're a rogue operation, most people don't even know they exist, and part of the reason for that is because they run out of small prefab bases, like the station mentioned in 13. And that's the smart way for a covert ops organization to run. Why are they suddenly posting up calling cards everywhere and making their own unique stations when their entire goal used to be being invisible?
15: Where the fuck did the Illusive Man Come from? Seriously, we raid 4 different Cerberus operations in ME1. In ME2 we raid precisely two Cerberus facilities. In Mass Effect we get outgoing messages to someone, but they're never named. Two years later and the Illusive Man is now getting his code name splashed everywhere and everyone has heard of him, whereas two years ago no one even knew he existed.
16: Why can't you tell the Illusive Man to go fuck himself? If you're a survivor background character he fucking destroyed your life, if you're not you've certainly seen the wreckage he created. He waves this off with a claim that they were rogue splinters, but when you think about it, if every encounter you had with an organization involved their "rogue" membership, and you're as (allegedly) well educated in black ops as Shepard, the term that comes to mind isn't so much "rogue" as "plausible deniablity".
17: So why are you working for this guy? You can't stumble back to the council half dead and ask to work with them?
18: How come the only time anyone activates the robotic defenses in this game is when they're trying to kill you?
19: How is it, the first thing you do after leaving is run into Tali? I know she's a popular character and all, but it's been two years, you've been dead, and literally the first living person you run into after coming back from the dead is an old buddy?
20: Why was a civilian colony outfitted with multiple anti-vehicle attack drones?
21: Where were Freedom's Progress' Drones during the collector Attack?
22: Why does Shepard mock us with an Assault Rifle in the cut-scene before facing down against the YMIR Mech? And, more importantly where does that rifle go afterwards?
23: How did Cerberus manage to build an advanced version of one of the most advanced star ships out there. In fact the SSV Normandy explicitly used alien technology that humans hadn't been able to get their hands on yet... how the hell did Cerberus manage to build that ship, and do it in secret?
24: How is the new Normandy not seized by C-Sec the instant you dock at the citadel? This is the equivalent of al Qaeda landing at an airport with a B2 and then being allowed to leave with it, coming and going at will.
25: Why wouldn't you work with the Council? Or, put more clearly, why the hell other than a plot hole the size of Wisconsin would you not agree to switch allegiance back to the council from Cerberus!?
26: Why the hell did Chakwas sign up with Cerberus? Remember, she was there with you, she saw reports on the things you saw, and all the hideous things Cerberus did. The justification she gives is she was bored by living planet side. Really? That fuckin' bored!? So she signs up with the people that were engineering bio-weapons and testing them on humans?
27: How did Miranda throw you out of your office? (I kid... sorta...)
28: Is Shepard being oblivious or darkly sardonic when they tell the looters in the quarantine zone that he/she doesn't like grave robbers, while (probably) having spent the better part of their trip there doing exactly that?
29: Why are the collectors working with the vorcha? This is the only time in the entire game we see the collectors working through intermediaries. Now, if you're following the sequence the game recommends for recruitment, the significance of this isn't immediately apparent. This is the only time we see the collectors doing this. Throughout the rest of the game they act directly or don't involve themselves. With the exception of this, the collectors are a bit like the Borg. They don't care about the details the individuals or what you're doing, so long as it isn't getting in their way, or you aren't something they want.
30: So what is the point to this entire vignette? The collectors have no follow up, and aren't involved in any other recruitment missions.
31: Every time I play Mordin's recruitment, I could swear there are krogen in with the Bloodpack, but they aren't immune to the plauge, so what gives?
32: So when Shepard asks the Illusive man to help him/her put his/her team back together, the one from the first game and he blows Shepard off, why does he then turn around and send him back out after Garrius immediately? Either he is genuinely incompetent (which is possible) or he was messing with Shepard (which is more likely) or someone dropped the ball (which is the reasonable explanation.)
33: If you take Zaeed on the Archangel mission you get some wierd blue suns dialog. It's not really a plot hole, but it is a crappy play at keeping the reveal for Zaeed's loyalty mission a secret.
34: (slightly out of sequence) why can't anyone patch up Garrius' armor? Now, I get that his face is pretty baddly messed up from the blast and all, but there's a freakin' hole in his armor now, and no plausible reason not to repair that, even if it's a patch job. What's more his loyalty mission gives you a palette swap of the exact same armor with the exact same hole in it. The only way to fix it is to spend three bucks on one of the alternate appearance packs. I know plot holes aren't supposed to be literal holes, but goddamn.
35: What the hell was TIM smoking when he thought getting Jack would be a good idea? I don't mean she's supposed to be dangerous, or unstable, though there is that too. She brings nothing to the table you don't already have, in the range of specialists.
36: Jack. Just fuckin' Jack. There is nothing about this character which makes sense in any way shape or form. She is a walking plot hole. As 35 mentioned there's no reason to recruit her. She's more of a liability than an asset. She actually wants to kill everyone on the ship. Oh, and she's psychologically impossible. The back story that's presented for her does not make sense. I don't mean I'm missing parts of it, I mean her experiences would not, and could not, produce someone with her psychology.
37: How stupid (on a scale of 1 to 350) is Warden Kuril? He knows Shepard has his/her weapons. He knows Shepard is so bad ass that even a little thing like being fucking killed couldn't stop him/her, he knows that Shepard is being backed by someone very fucking powerful and resourceful. What the hell was he thinking? Bonus points if you bring Zaeed along, in which case you've got his former boss along for the ride as well.
38: What kind of a stupid prison even includes an "open all cells at once" button!?
39: Why don't the Blue Suns on Korlus have duress codes? Okay, that actually kinda makes sense, but anyway.
40: How can a krogen be put down as easily as Okeer? Maybe he had some kind of condition? But with the psychotic ecosystem that produced him, krogens should be incredibly resistant to toxins.
41: How much brain damage did Shepard have to suffer before opening the tank and letting Grunt out? There's overconfident and then there's suicide. This is not the former.
42: Where did Mordin get those seeker bugs to play with? This really strikes me as there's a cut mission someplace in here where you went in and got these things from someone, (maybe Okeer?) that got cut.
43: Where are Horizon's Robot Defenders?
44: Characters who were not party members in the first game will talk about your experiences on Eden Prime. If it's Miranda, Jacob or Mordin, this makes some sense, but how the hell would Jack and Grunt know what you faced where. Jack's lucky if she can remember what she had for breakfast and Grunt may not even be literate (or housebroken) yet.
45: Assuming Direct Control.
46: How is "I was dead" not a legitimate reason not to ring up your old buddy? Seriously, it's entirely possible to spend the first few hours trying to find out where Kaishley is only to be stonewalled by Spawn Anderson or Udina.
47: Why the hell would Tali care about how Shepard got to Liara in her recruitment mission in ME1... and more importantly what the hell does it have to do with anything regarding her recruitment? To explain, she talks about using the mining laser in Liara's recruitment in ME1, but that doesn't have any applicability to this situation where Tali is using demolition packs to clear away rubble.
48: So the sun fries all electronics, but not the geth, and not your weapons, but it does fry the quarian's weapons? Oh, and bugs, it fries bugs good too.
I'm going to cut it here, I've still got plenty of material to munch through but I'm actually getting tired, so I'll pick this up again later.