When trying to improve Soulrivers' run, I stumbled upon a bug in stage 7. It's useless there, but it I managed to abuse it in stage 4. This bug lets you go through walls which are only 1 tile wide. (If you use it in a wall more than 1 tile wide, it's useless.) Note that if you are inside a block which can fall down (or presumably a rock, but my brief test failed to push myself into one), you die, so this bug doesn't apply there.
WIP completing stage 4.
Also, falling off a platform gives exactly the same 1-pixel boost as jumping.
EDIT: I confirmed that glitching inside a rock will kill you. It seems that you can't glitch into ground-level blocks (ground level where you enter the block, not where you start the jump) unless the space above them is blocked.
Smashing blocks by headbutting them instantly moves you next to them, so it's the fastest way to travel when applicable.
And since I'm here,
WIP completing stage 10.