I quite enjoyed Mass Effect, but I had a few major nitpicks that drove me absolutely crazy.
1. Combat. Yes, it's an RPG, but the combat model didn't have to suck quite so bad. In fact, a first-person mode for combat would have made it infinitely better to begin with.
2. Tedium. Most of the transition between story points was drive here, shoot Geth. Drive there, shoot more Geth. Shoot a few Rachni just to add a little interest. Aha, drive there, now shoot more Geth. Wash, rinse, repeat. It got really tedious.
3. Level design. Seriously - how hard would it have been to hire ONE FREAKIN' GUY to mix up the level design on the non-plot worlds? It was simply disappointing how they re-used everything. This was probably my biggest pet peeve.
4. The Interface. While level design was my biggest pet peeve, the interface was the thing that had me wanting to quit playing. Seriously, what moron designed that inventory system? Especially the barter system, good grief. 150 items and no way to sort them, AND they don't even display alphabetically. Made me want to shoot the damn merchant. Except... oh right, I can't. BLARGH!
5. Elevators. I played this on the PC and the elevator rides were ridiculous. I can only imagine the pain of console players.
6. Annoying inability to save during combat. OK, I know, it makes it tougher and more of an accomplishment to get through battles, but I got really tired of cleaning out an entire room only to have some jackass with a shotgun+carnage come running around a corner, through my allies, and blast me twice in the face before I could get a Barrier up. THAT bugged me.
Those things aside, there were a couple things I thought were done quite well.
1. The leveling system. After playing Oblivion after Mass Effect, it made me really appreciate how they handled levelling up. While Oblivion's system may be a little more realistic (practicing skills increases proficiency in those skills), I'm not looking for realism in an RPG. I want immersiveness. Being able to actually customize my character as I played through according to my wishes rather than because I had to use one particular weapon was a serious blessing, and it makes you much more involved in who your character becomes (I was a Vanguard, and I maxed out my Biotics pretty quickly, most notably Throw and Lift, which are infinitely useful if fighting Geth Colossi on the ground, as I did frequently for the extra XP
2. Freedom. After the introductory levels, you can pretty much go anywhere and do whatever you please - but, you might get your ass kicked because you aren't quite the galactic badass you become 3/4 of the way through the main plot. I lost count of how many times I died on Phoenix trying to rescue Wrex's armour while at level 4 (it was the first planet I visited after the Citadel).
3. Integration of companions. Mass Effect was my first party-based RPG, and I had always stayed away from the genre previously because the idea of managing a party didn't appeal to me. Mass Effect let me play it like I played through Deus Ex and System Shock 2, which are my two favorite games of all time because of the combined FPS and RPG elements. Companions were integrated into the story and missions, BUT I didn't have to micromanage their abilities. That said, I would have liked a little more control over them than the interface allowed simply because I wasn't toting a sniper rifle and some missions got really frustrating because they didn't follow orders well. Fortunately, I upgraded my pistol as much as possible and the marksman ability made up for the lack of sniping.