I've seen a couple of design problems with levels.
One of which is overly reliance on tight jump with landing spot being only two tiles wide or in some cases only 1 tile. Into The Stars level is guilty of that in particular as well as one of the levels after it the name I've forgot for the moment. This, combined with Tux's relatively high inertia makes for some very frustrating platforming where you'll fall into a bottomless pit more often than not. The solution would be either redesign problematic parts to be at least 3 tiles wide or decrease Tux's inertia so that he can come to a full stop on normal (non-slippery) tile in distance being less than a tile without any input.
Another is the fact that on some levels if you lose powerup, you're screwed as they're almost impossible to complete as small Tux. Every level should be completable as small Tux!
The situation is so bad that in some cases once you lose powerup status/die in bottomless pit it's easier to just hit ESC, select Abort level and then go back to Welcome to Antarctica where you can easily farm both fire flower and big Tux powerup, then return to the level you're actually trying to beat.
Just for your consideration.