Combat normally gets put in to a single bullet point in threads like these, but the combat in ME3 was really master class.
ME2 managed to transition a more numbers based RPG combat system in to a very solid third person shooter. Hell, that battle system was fantastic as it was, but if anything, the RPG mechanics had become too simplified. While the rock-paper-scissors strategy behind finding the correct type of power to cut through different types of enemy defenses was sound, at higher difficulties it neutered biotics based on physical effects (throw, pull, etc.). Movement, while never a strong suit in ME1, still felt very rigid. The revamping of the cover system was a formative moment that moved Mass Effect from a good, ambitious RPG to the fantastic series that it has become.
That being said, ME3's combat really outpaces ME2 in every way, and I think it is easy to take that for granted. Personally, I was very disappointed in how weak biotics felt in ME2. Anything with a shield, barrier or armor (literally every enemy on Insanity) couldn't be physically affected by biotics, and by the time they were down to just health, in most cases gunfire was still the most effective way to take them down. ME3 cut back on the defenses, and seemed to place them in more logical situations. (Armor still shouldn't be immune to biotics. That makes no sense, as far as I'm concerned.) Shepard no longer had to sidle from side to side to awkwardly dodge slow moving projectiles, and the ability to move from cover to cover was a godsend. The shooting became more visceral, and biotics once again gave the player the feeling of having a supernatural advantage over their opponents.
That being said, it could be even better. As of now, movement is still somewhat limited. I've liked what I've heard in the leak about upgrading mobility. I think that tech powers and biotics have started to overlap too much. You might have noticed I didn't mention tech powers in my 'pro' section. Outside of the two main tech powers (Tech Armor and Tactical Cloak), many tech powers feel just like defense strippers. This would be fine, if it weren't for the fact that biotics often perform the same function. I would like to see tech and biotics function more differently next time around. I'd like to see biotics function in a more crowd control way, and tech powers retain the power stripping capabilities, with a few more tactical advantages. (The multiplayer laid out a nice base for this-- Turrets, Shields, Hammers, Jets... There's some different playstyles there.) But really, there's not too much to be done, combat wise.
Long story short:
Like
Better power balance
Better maneuverability
Greater enemy variety
Greater weapon variety
More expansive RPG mechanics (leveling, armor pieces)
Don't Like
Tech powers seem redundant to many biotic powers
Shepard is very 'grounded.' It seems odd for a person capable of launching a Krogan 50m to still have to use a ladder.
Some powers are game breaking. Tech Armor can be abused pretty terribly. (Take Nova as a bonus power, then use tech armor, immediate use nova to have an extra strong nova with a very small cooldown. While you can always just not use a cheap tactic like this, I'd like them to tighten it up so it isn't even possible. Balance is key.)
....Yeap.