I'm pretty sure this is going to be a rather subjective topic and there are going to be a lot of conflicting opinions about it, but who know maybe something nice might come out.
I think there are a few little things that might improve how the movement feels in the game, but whether they would be improvements is debatable of course.
-I think there should be a short acceleration/deceleration from standing when the player moves left or right. It shouldn't be too much, just a tiny bit. Maybe the character moves the character's width before reaching full normal walking speed. A lot of platformers have a tiny bit of this (it's often rather subtle) and I find it helps with making small adjustments to your position as only briefly tapping left or right doesn't move quite as fast as holding, and it might make the movement feel a bit more fluid.
Ok scratch that one, apparently it's already somewhat like that but my previous character had such a speed boost that the acceleration wasn't noticeable. I started over with a new one and it seems to work this way now.
On the other hand, maybe it might need to be made a bit more apparent in that case? Eh, not really sure on this one.
-Related to the above crossed out item. I tried several characters and it seems that modifiers for movement speed and jump may have unintended side effects on how the movement feels in the game. When the player starts a game for the first time, they won't know what the effects of these values will be, and since each game will use only one main character they won't know until they start another game. I'm slightly concerned that some people's impressions on the game's movement may be adversely affected by this.
I don't remember what stats my previous character had, but I'm now using one without any movement related bonuses and penalties and it feels MUCH more natural than my previous one while my previous one felt rather clunky.
-I'm not that sure about this, but I'm starting to think the player character falls bit too fast. It feels a bit difficult to line up shots when jumping because of how quickly the character rises and falls and the way they accelerate. I also notice that the way jump height is controlled feels a bit all or nothing (is it?). I think it might be beneficial from being a bit slower and slightly more "floaty" (is that word appropriate?), and how long we hold the jump key should perhaps influence jump height more.
Thoughts?