I was excited to see the remake after having played the original back when it first came out. This remake was amazing. I had fun playing it through a few times. However, I did find a glitch while playing.
While in the tree (where you need to jump and get up to the top) and the first part after exiting that stage, if you die and get a game over, and choose to replay, you respawn in the wall of the tree with no choice but to go right and fall off of the map into nothingness.
That was the only problem I had with the game. Hopefully you will get that fixed.