There are a few major new/changed mechanics that we currently know of:
Random tripping has been removed; forced tripping is still in.
You cannot grab a character if you've thrown them in the last second (no chaingrabs).
There is no longer a difference in edge actions upon reaching 100% damage.
Edgehogging has been removed; instead, the incoming character will steal the edge from the current occupant.
It appears that swimming has been removed; characters will just fall through water as in Melee.
Directional influence has been revamped. In previous games, you could change the angle of your knockback by holding perpendicular to it. In SSB4, you instead add a vector in your holding direction, which can alter both your angle and your distance.
Characters at high damage deal slightly more knockback.
Best Answer
Just tap up on the joystick to cancel the Super Dedede Jump.