Another good example on how bad the actual details of the science are in most of Star Trek.
Warp moves you by compressing the space in front of the ship and stretching it behind it.
Your frame of reference in the middle of it stays at rest.
So no stains on the wall.
Impulse power would be a completely different thing, though.
But even that the writers managed to get wrong most of the time, treating it like a kind of fixed absolute speed that you achieve, like the max speed of a car, instead of the steady acceleration capability it actually is, with no max speed besides relativistic limits.