I think the problem I had with the jump physics was that the jump height depended too much on how long you hold the space bar. If you just tap the space bar, you don't jump very high at all - but if you hold it down for the whole jump, you jump almost four times as high. This sort of physics can work well if you're having to do lots of very small precise jumps, but it doesn't work as well if you need consistent big long jumps (as you often do in this game). And it doesn't fit well with a double-jump mechanic, since you want to keep holding the space bar down through the whole jump, but you also need to release it and press it again to trigger the second jump.
I'd have preferred something along the lines of: short tap gives you 75% of maximum jump height, slightly longer press gets you 100% jump height, and you've got time to release the key in time to press it again to trigger the double jump. If that makes sense!
Also: I love the walnut's bow tie :P