Well, this certainly needs some work.
1. Don't have the music overlap.
2. When Mario is stationary and on the ground, have him return to a standing position.
3. When the sprite flips, it moves a significant amount, probably because the sprite is off-center.
4. On one frame of the walking animation the sprite "pops" up a little.
5. Speed up the frame rate of the walking animation so it doesn't look like he's gliding over the ground.
6. Add "dulled" aerial control using not a sprite.x++ command, but implimenting a "velocity" variable and having aerial control add/subtract from it as the directional button is pressed. You should have Mario be moved constantly by this variable, but have handlers that set it to 0 when you want him stationary. This will also allow for accelerative ground movement as opposed to an instant velocity change.