The most dated and painful aspects of COH of course.
I would make attacking while moving something that every melee character can do with all melee attacks, and some ranged attacks would also be useable in motion. I would ditch the painfully janky hard tab targeting system for a soft lock system, you point and fire off a power, and if it hits it hits. Softlocks would mean you could ensure which target you focus on without it deciding to target that one guy on the other side of the map when you're trying to melee.
Things to keep are of course the actually unique aspects of COH, powerful buffs and CC, nontraditional roles, and so on.
The combat mechanics themselves though are not unique and are nothing actually that fun in themselves. it could be SO much better but its held back due to when it was made.