The combat is by far the best in the series. Not jerky and generally shit like ME1's combat. Not over-reliant on cover-based shooting like ME2's, with a much wider range of more challenging enemy types to boot, and a wide selection of guns and upgrades that all feel unique, rather than getting a rifle that is just your current rifle +1 of everything like in ME1. Powers are all fun to use too.
The multiplayer is legitimately good, although it could really use some more game types beyond just adding a few more round types to the current horde mode. I also really like the feel it gives that it really is the whole Galaxy that's at war now, not just Shepard, and that everyone has to play their part in keeping the Reapers at bay if anyone is going to survive.
The progression and stats in my opinion found the perfect middle ground between the first two games. ME1 was bloated and tedious to the nth degree in that regard, whereas in ME2 it was so cut down it might as well have just not been there. ME3 found the sweet spot.
Moments in the story (if not quite the whole story arc in itself) that are simply sublime and perfectly executed. Necessary mentions go to Mordin, Thane, and Legion, but there are more as well.
I like how the vast majority of the characters we know and love each get their moment of glory, without the squad numbers becoming too large (that said, just one or two more wouldn't have gone amiss), as well as introducing us to new characters rather than just relying wholly on established connections. Also, I like Vega and Javik. YEAH, YOU HEARD ME!
Finally, post-Extended Cut I actually like the endings. The theme of the ending is clearer, I approve of it, and most importantly it now actually feels like an ending to a story, where your actions (whatever they were) made a radical difference to the world, with a nice goodbye scene to finish the whole thing off (I seriously broke down at the end of EDI's narration for the Synthesis ending and I'm not ashamed to admit it).
Other than that... Grrr bugs grrr auto-dialouge grrr animations grrr ret-cons grrr!