Ok, so I just gave it another try and I realized it was just me beeing stupid. It didn't come to my mind, that you are supposed to dash midair. So I assumed the pipe is in fact a platform, as there is no way to get past it without dashing. It was late yesterday... :D
I haven't made it to the end yet, but it is definitly fun to play. The only thing I really missed was checkpoints, so you don't have to start all over again when you die.
There are some problems with the dash though. Is it possible, that this is framerate dependent? Sometimes I move to fast, I can't even see my character and instantly die. I assume you update the charaters position in the Update() method? If so, make sure to multiply the distance with Time.deltaTime. (Didn't really have time to look into the source)
Also there are some weird interactions when pressing jump and shift together. In general shift seems to increase the speed and uses the current player's direction, which can cause the dash to either not work at all or go up or down instead. Try overriding the player input with the player's facing direction to make the behaviour consistent. ;)