many people try to go too much around puddles, bits of mud, rocks, ... Switching direction is what makes you slip/fall.

Sometimes, you should just focus on going straight, or at least keep your center of mass relatively going in a smooth line.

Yes, sometimes that means going through a puddle or do a small jump, but I find it much safer. Of course, on a potential slippery surface, try to make that 1 step lower impact, basically like an in-between step. This can also imply vary big changes to your cadence, which is not always optimal from aerobic perspective.