Does GMing improve an individual's playing? Does playing improve a GM's GMing? In what ways? Why? If not, why not?
I was all for saying yes in both cases, then I asked Lou this question. I like sharing these questions with him, it helps me think of things that I'd forgotten.
He reminded me that when you have been a GM but now you're playing a game, you can be more critical of the GM than a non-GMing player. You might be more likely to see where the GM made a choice you wouldn't have, or they're not handling a situation right (in your opinion, of course).
I do think that it can help. You don't always have to think with your GM hat when playing. But if you GM, you know what it's like to sit behind that screen (or whatever). So when you're on the other side, you can appreciate the hard work the GM put in, and can appreciate the story he or she is trying to tell. And might be more willing to help them achieve their goal.
Now, does playing improve a GM's GMing? I think it can only help. Again, seeing things from the other side of the screen is good, it helps you realize what the players are thinking when you're GMing. I don't know very many people who only GM, and I can't imagine not playing, so this is hard for me to imagine. I do think it could help the GM make their NPCs more than just one-dimensional characters, because you've had to (hopefully!) make your own character as a player become three-dimensional.
Gah, I'm rambling now. But I think I've covered everything.