How do *you* run?
I have two more problems to add.
Scope and pace is a huge problem. The game starts, everyone is enjoying themselves, and then the GM says a fight breaks out. You go into turn based combat and the game basically collapsed because you go from posting complex actions once a day to posting a single task once per week. Or the GM wants to start some 1-20th level style epic without realizing the much slower place of pbp.
The only way I can think to not fall into these traps is to not do it. If you have to have a fight, it's probably best to resolve it in a round or two (a few days) so you can keep the game going. When planning adventures, you have to make them much shorter and simpler, since it could take months to play through what you can accomplish in a session or two in live.
The other big problem I've seen is what I call babysitting. Some published games have a lot of back and forth between the GM and players/players and other players. In a live game, it doesn't take more than a few seconds to ask the GM for a roll modifier or to adjudicate something, but in pbp, that can take a week.
Again, the only solution I can think of is to not do this. For example, I love FFG Star Wars, but do to the constant back and forth needed to build dice pools and declare rolls, I have no idea how people play it by post. Freeform games do well here, but there are published games that don't require this kind of babysitting.