Since I'm sure a game as polarizing as Dragon Age 2 will have plenty of people posting what they didn't like about it, I'll instead focus on what I thought it did right.
Story: The story was really great, especially as it wasn't another borderline cliche 'Save the World/Galaxy/Nation' thing. The mage/templar fight was, for the most part, well done, and I want to see more of it.
The characters: Seriously, I don't think there was a dud among the DA 2 companions. I didn't love them all (seriously, I wanted to kill Anders byt he end), but I wasn't indifferent to any of them, and that, I think, is the mark of good writing.
The idea behind the setting: A lot of people zeroed in on having the vast majority of the game being set int he same city, but I liked it, at least in concept. While the execution was lacking, the idea of getting to know a single city ofver the course of years is a worthy one, and I hope it rises again. Kirkwall's story and history were fantastic as well.
The combat: While I'm not sold on the combo system of DA 2 (I preferred the spell combos of the first Dragon Age), I liked the way combat was updated overall. Combat looked a lot more interesting, and the addition of an optional button mashing attack made low level combat, where you're likely to only have one special attack, and that on a signifigant cooldown, much more palatable. Again, the emphasis is on 'optional'. The thing that made it good was that I could swap to a standard auto-attack once I got to mid-levels and had the toolbox to focus on strategy. Also, making fighting with a shield badass.
Varrick: That's it. Varrick was awesome.
The new looks for elves and Qunari: While I appreciated what the artists were trying to do in the original, I vastly prefer the look of the DA2 non-humans, Darkspawn, who looked better in the original, excluded.
Voice acting: I never really realized how much VO added to DA until I went back to DA1 to finish an import file.
That said, I'm pretty sure it's against the law to talk about DA2 without ragging on it, so here are soem things that positively drove me up a wall.
Recycled environments: Need I say more? Dungeons, caves, dwarven ruins, didn't matter, they were all the same and it SUCKED.
Kirkwall: Like I said, I liked the idea of getting to know one city over the course of years, but that ONLY works if the city actually CHANGES. And no, having it on fire at the very end doesn't count.
Story: I like the overall idea of the mage/templar conflict, but if that's going to be the focus of DA3, there NEEDS to be some actual moral ambiguity. As it is, we see bad seeds within the Templars, sure, but it's hard to blame them for their extremism, given that nearly every apostate mage we meet in game is A: a blood mage, B: an abomination/about to turn into an abomination, C: an evil necromancer, or D: none of the above, but going to attack us anyway. As it is, I felt guilty for siding with the mages in DA2, and was honestly glad that I got to kill Anders. Justice would, I'm sure, have approved.
Companion characters: Specifically, not being able to respec them as you see fit. What's that, you don't like Avalene? Or maybe you foolishly decided you wanted your character to be tank tank? Too bad, Avalene is forever and always a tank. Don't like Anders? Too bad no other mage IN THE WORLD can be a decent healer. Like I said, I killed Anders. You can imagine how much fun the end of the game was without a healer. Speaking of Anders, at least if you didn't want him to heal he could be a decent offensive caster. Too bad Bethany and Merrill couldn't do the opposite.
Not being able to choose my race: Pretty self-explanatory. I want to be able to play as an elf or dwarf or even Qunari in DA3. Also, I still want full voice acting. I'm tough to please, I know.
DLC: Seriously, some equipment packs and TWO measly adventures? Not cool. Awakening was beyond awesome. That's what you should be aming for. Less Horse Armor, more Shivering Isles, okay?