I do agree you occasionally seem to miss a note, but I think that's mostly because in the games' version they used more instruments and here you're trying to do everything with a piano which is tough. It's never really a biggie, but at 00:54 it does bother me a little. Those higher notes you hear just before that moment (I think it's Mumbo's xylophone that plays them in the game) are actually played again by a flute, but you only play them once and then you go over to only doing the banjo again. That part just sounded weird to me.
In order to improve it, I think it might be an idea to re-record the song a couple of times and only do one instrument on each. Then in the end put it all together, edit it a little and you might have the full song covered on the piano which might turn out really nice. Otherwise, you could perhaps consider adding an extra instrument.
Overall 3.5 out of 5. You covered this song pretty nicely, but there's still room for some improvement in my opinion.