There are some doors that I have no idea how to get to:
Above where I'm standing in this screenshot, there's a red carpet floor. There's a door there, and a door just to the right of that and up a bit.
How can I get up there?
I finally figured out how to do this. It's easier as Dustkid, but I was able to do it with Dustman also.
You want to jump up the left-most wall. Jump from the platform with the bust on it, then run up the wall, jump off and then back onto the wall, then run up it again. At this point, you want to be right at the corner where the vertical wall turns into the 45-degree angled wall. If you jump off the vertical bit while holding up, close enough to the angled wall, you will run along the angled wall as well, giving you a 3rd wall run even though you used all your jumps. This will be enough to land on the platform above.