Bards: More skill and knowledge stuff. Right now they feel so focused on compositions that they lose out if they try to make something akin to the Archivist or Archaeologist of 1e.
Rogue: DUAL SLICE. Why the hell is rogue lacking a feat that enhances multi weapon fighting? Make it only for finesse rogues if you don't want brutes or swashbucklers using it. Make it a later level than fighter/monk/ranger gets it. Make it so it does fewer dice of sneak attack of you think that's too powerful (even though it's really not). Just PLEASE let rogues get it without having to multiclass. Dual-dagger-wielding thieves or ninjas are very iconic to fantasy adventure games, and it's a shame they can't embrace that in 2e.
Paladin: let them be something other than strength based heavy armor characters. I'd also love to see more alignments accessible.
Ranger: make crossbows better!