Jumps: It turns out that jumping temporarily increases your horizontal velocity. So, when walking over flat surfaces you should jump whenever it is possible. Works whether if you have a ceiling overhead, or not. Each jump like that saves about 0.20-0.25 second (with no ceiling).

Falling into "pits": When you are about to fall from a high place to a lower place, it takes a little time to build a vertical velocity downwards, when you leave the ground. So, if you jump when reaching near the fall, you will reach the ground level with a full vertical velocity, and fall the rest of the distance faster.