I have an idea: what about an ability of choosing a level you completed before in a save file?
Also, when you die and respawn at a checkpoint, the Shoe Goomba Coin progress doesn't save.

Also, the Mario Forever version of The Lost Map's 5th level uses another soundtrack (remix of Waluigi Stadium).
(I was the second person who downloaded this demo, yahoo!)

This is a pretty good traditional-Mario-style game. I've yet to beat it, but there were a few issues I've noticed so far.

-During the Boom-boom fight, I would get hurt if I stomped on him while he was jumping. It seems you can only stomp him safely if he's on the ground.
-I think an in-game prompt to ask you to save between levels would be beneficial. In the era of auto-save, it's really easy to forget to press S during the level intros.
-It's really easy to get blind-sided by the falling blocks in 1-7, especially when you're first playing the level. I think it would help if you could telegraph them better besides the slight change of color. Maybe have some debris fall down from them before they actually fall or a sound play before they fall or something to that effect.
-I do think Mario's controls could be improved a bit as he does feel a tad slippery. Maybe reduce his acceleration slightly? Maybe also make him turn faster while changing directions in the air, so it's easier to correct jumps.
-I find the moving platforms in 1-4 to be annoying. The window you get to jump on the next platform above feels too short. It's nothing too bad, but I did find these sections tedious. Tweaking Mario's air control and/or adjusting the timing of the platforms could help with this.

With all that said, this is a pretty solid demo. There's a good variety of level themes and power-ups, too. I liked the leaf-falling effect when you kill the piranha plants. I look forward to seeing this game expanded on.

thank you for telling us about your impressions and problems of the game, I’m already working on fixing some mechanics and the listed problems in general, perhaps I’ll release a patch or a complete new version with problem fixes and new content)