Character mistake: Michael states that if you touch someone being tasered, you'll be tasered too. That's not true unless you touch them right between the probes. And in a later episode Michael's touching a man being tased with no ill effects.
Character mistake: Near the end, when Michael reveals to Brennen he knows everything about him, he says, "I know everything about Tyler Brennen." Michael emphasizes "Tyler" as if it's a big deal that he knows Brennen's first name. Michael already knew Brennen's first name from the first time he met him, in Season 2, Episode 15 "Sins of Omission."
Chosen answer: It might not actually have one, in which case, he'd have to go down into the club and use theirs. As for showering, going to his mother's house or a gym membership would take care of that.
Captain Defenestrator