I've tried to use the platforms well:
And I have some basic jumping puzzles implemented:
Finally, I mapped out where the boss fight will take place:
There are still large areas of the level that haven't been designed, but I'll get to those tomorrow.
I'm still getting the occasional "Fall through the platform" bug, which is quite annoying. I've come up with the most probable reason why those bugs are happening.
My best guess is that if the player jumps on a platform from too great a height, and since the player accelerates as it is traveling down, it completely bypasses the platforms collision rectangle. That is the only reason I can think of.