At the end of the Cloud Bridge section of the first level there are two puzzle pieces. How do I reach them?
It's been a while -- have you tried jumping on the platform inside the picture? (The one that is itself on the puzzle piece) It might look like just another jigsaw piece, but it'll support your weight just fine.
Move it around until you're able to jump from the platform to the left of the puzzle to the right side of the puzzle. This'll let you reach the top jigsaw.
I remember less about the puzzle piece directly above the exit door. Looks like you need a Goomba, which you may need to "escort" to the end of the map via moving the puzzle-jigsaw platform, as for the above piece.