Your collision detection could use some work. Accidentally falling through platforms because you're falling too fast isn't a good thing. Also, some of the boxes end up floating off of the platforms, making certain areas impossible to reach (like the bird, for instance).
You should probably either not allow people to load the trophy room while the next level is loading or have doing so cancel auto-loading the next level. A way to turn off the "you can't do that" popups would also be nice. Overall, well done, though.