The check points don't work for me but, other than that, this game is amazing! The level designer clearly knew what they were doing. It starts out extremely easy and gets progressively harder- always building off of previous concepts and never getting repetitive, over staying it's welcome, or completely throwing away old concepts.
The tiles and background are amazing. I don't usually care what characters look like in a game but, in contrast to the effort put into everything else, the ugly character sticks out like a sore thumb and it's disorienting XD. Aside from that, I absolutely love the art style!
One thing I think could definitely improve is the health system. Early games had hearts/lives because they were designed to eat up quarters and it's become an unquestioned standard since then. Most games would do much better with an alternative penalty system. With this game, it definitely detracts from the experience. Just having to restart the level you're on and try again to overcome the obstacle that stumped you would be penalty enough without messing with the flow of the game.
The extra heart containers you collect as a reward for completing extra little challenges wouldn't be obsolete either- they could easily be replaced. That being said, the way this game builds off of each concept it introduces rather than toss them aside to introduce new obstacles allows you to easily recover lost progress.
Edit: I just realized this game is showing as a 3 star rating even though every review on here is 4-5 stars. A bunch of people are giving it a low rating out of shear spite for the fact that it was too hard for them. A lot of people are going to miss out on experiencing this platforming masterpiece because of sore losers and that really sucks.