So, I waited quite a while to reply here. In fact, I gave it about two weeks. Read a lot of the posts here to get "inspired" and let the trilogy play out in my head. After all this deliberation on what part of the gameplay in all three games really annoy me...
...I got nothing. 
I really can't think of any part of gameplay that annoys me. The run, gun & power gameplay got improved with every iteration of the game but even back in ME1, I love it for it's own reasons (stronger impact of the RPG component, over the top awesome biotics, etc.). Later on it just became super smooth and polished.
I also love driving around in the MAKO. I know that a lot of people complain on how stubborn the thing is but at least on PC, I never had many problems. I actually think a lot of people play it "wrong".
I find it fun to look at the maps and figure out the best route to get to my next target that is short but also avoids the worst terrain. Most of the UNC map actually have kind of secret pathways and optimal routes built into them and if you figure them out, you can make your UNC exploration feel like a Sunday drive
. It's certainly no random height maps.
And yea, of course I will also utter some foul language when a threasher maw one-shot kills me by emerging right under my MAKO but it happens maybe once or twice in a full playthrough so no biggie.
Also liked the Hammerhead. Sure, fighting with it is awful but thankfully, there is hardly any of it, so it doesn't annoy me and the platforming sequences are just long enough to freshen up the game but short enough not to annoy.
Mini games: I liked those too, especially in ME2 because, while they were a bit repetitive, they could be done really quick and it kinda felt like you were actually performing the action (I always imagine Shep with one of these little laser pen things from star trek really hotwiring a chip when I do bypass
). So no annoying at all. The mining in ME2 isn't really a problem either once you have an idea how much minerals you actually need an spread it out over the entire game time.
The turret sections in ME3, yea, they are not exactly the pinnacle of game design but I get what they are about and why the game would probably be worse off without them. Also, I don't mind shooting from a turret from time to time.
So all those little things work for me and I love the general gameplay. I really can't think of a segment of the games where I would get to it and say "Oh no, not this again". It just doesn't exist for me. Hm, I never realized that until this thread came around. Well done BioWare I guess. 
Now, I'll head back to the story threads where I can complain about stuff. 