Head on over to the EM residency forum for more replies. IMHO August through Sept are good times. The conventional wisdom is that, at institutions that have all interns in the ER in July, that July is a bad time. Otherwise people have had good luck with July too. If you're not looking to get a letter from the place then anytime before match lists are due can be good.
But make sure you can hack it, because if you're a slacker, then auditions can hurt rather than help you. I know a few of my classmates who were discouraged from doing auditions based on past evaluation of their work ethic.