Okay, I would have to say that Mass Effect hands down is my favorite series of all time. It has deeply affected me more so than any other game out there has managed to do, as it taught me that video games could be a medium of great storytelling and real heart. I could write entire dissertations on the implications of some of the in game history of this series. However, there is an asymptotic relationship when something approaches perfection where the flaws just seem to jump out more and more.
For Mass Effect 1 I agree with pretty much everything Robot Number V said - inventory is bollocks, the side missions are same-y and the Mako is...the Mako. The combat was also pretty wonky and at some particular points seemed almost unfair. Dat worldbuilding and storytelling though. It's a real shame Drew Karpyshyn didn't stay for the whole series; he's a fantastic writer.
For Mass Effect 2 The side missions were a lot different from one another but it did just feel like a shooting gallery most times. Enter a room, take cover, shoot some mercs. Especially at the beginning of the game, it just felt like I was shooting only mercenaries. I couldn't tell you the difference between Blue Suns, Blood Pack, or Eclipse (other than color) - they were interchangeable to me. And I agree with Rpground on the fact that I missed the Mako missions. They improved everything else so well, what stopped them from improving vehicles? It gave the universe real depth - made it feel lived in and fleshed out with a sense of scale. We just had that god damned scanning minigame instead. Also, did anybody get weirded out with the Terminator at the end? I feel like they wrote that whole 'reapers take on older forms' thing and then just dropped that plot line after that. Hell, in Leviathan DLC the Leviathan says all reapers take on Harbinger's shape, which makes a hell of a lot more sense as they all look basically like Harbinger. All the characters were amazing in ME2 though (except Jacob, of course), and they did a good job of saying, 'look your old squad is gone, here's some new guys'. Which, for me, I really felt like Shepard - I didn't trust these new people, they weren't as good as my old crew - until I started really diving into their stories and mannerisms. But this thread is about things we dislike about our favorite games, so I will get back on topic.
And, yes, Mass Effect 3's ending was awful (at first) then got noticeably better. Not because they changed everything, just because they explained it better. I wasn't one on the Bioware forums spitting vitriol, but I was sure watching it, generally agreeing with the angry populace, and I'm not terribly proud of it. But as I said, when the game is nearing perfection, or at least what you perceive as perfect for you, the flaws stand out so much more. That game, man. The combat was tight, the pacing was brilliant, the quiet moments were just as exhilarating as the violent ones, and it tied up so many conflicts so well! And yeah, I still get a little broken up inside when I think how ham-handed the ending was. For a story that started (and continued!) so strongly, to get that wet slap in the face was a real wake up call. Phoo. For anyone that made it this far in my post, thank you, it was nigh therapeutic to get that off my chest.