Is it possible for a "leg" to go bad on a 220 dryer outlet? I have a dryer that stopped heating. While I'm waiting for repairs, I plugged in another dryer. It also isn't heating, although they both run. Is it my bad luck to have 2 dryers that need heating elements or could it be the outlet?

It could be the receptacle, the breaker, a fuse, a termination,.
Could be several things, but it's probably not the dryer.

Suggest that you turnoff breaker and then turn it back on to maker sure that one side has not tripped.