1. Could seriously use a variable-height jump (longer-hold = higher-jump, or rather the inverse of that would be nice)
2. Having the music keep playing rather than restarting w/ the level would feel a bit smoother
3. Fix the small graphical glitches. Player floating by 1px, level spawning in when you start, etc. Makes the game look lazy.
4. Maybe store the high-score locally and display it on the main menu or in the corner while playing. Gives the player at least a minor tangible reward for doing well as well as a goal to improve.
Good proof of concept but I'm giving it 2.5 stars for now as there isn't much to it and there are some obvious graphical bugs that should have been simple to fix.