Jumpstart doesn't slide off edges in project m.
Sensitivity on the control stick for things like tilts/smashes/dashes/etc is a little different in project m. I'm fairly sure this is the case, gives me a hard time fluidly transferring my dashdancing between games.
Jab resets are based on a knockback threshold instead of a damage threshold. This is actually intentional and allows for high damage knockdown resets like luigi's dtilt as well as prevent that awkward hitstun/knockback/? glitch in melee where certain moves (falco's shine and falcon's side-b most notably) would launch a downed opponent with no hitstun.
Ledge grabs have one frame less invincibility, I think. Other ledge actions also occupy the ledge for less time, most particularly rolls. Ledge jumps can also be acted out of once the initial animation of leaping off the edge ends. These are all intentional I believe.
Momentum from walljumps can be shifted without interrupting the post-jump animation with an aerial, meaning repeated wall jumps by drifting back to the wall are improved since you don't have to do an aerial to start to drift back.
Various added mechanics like wallclings, RAR's, B-reversals, DACUS, etc.
Power shields of projectiles work differently than melee (I think?). If I remember correctly, powershielding projectiles in melee worked by shielding a projectile while it was in your maximum shield bubble size or something along those lines, whereas project m PSes projectiles for the first 2 frames. Not entirely sure on these details though.
Short hops are easier due to the window to release the jump button extending into the last frame of jumpstart in project m, unlike in melee where that frame was excluded from the window.
Dash pivots are easier as a tilt input opposite your dash direction will stop your character and turn them around immediately.
Ceiling bounces still work like brawl, at least that's the last I heard PMBR say about those.
Throws have static release points in project m whereas in melee the release point changed based on (I think?) weight or some other per-character basis.
These are in addition to the others mentioned. I'll add more obscure ones when I think of them lol. It's entirely possible that some of these are fixed already and I haven't paid attention well enough to notice, hopefully someone more knowledgeable than I will correct me if that is the case.