Audio problem: When Michael is forced to do "errands" for Brennen, they stop by Jonathan Carver's house to get numbers from him for a voice key. The code played back at the facility is 71348. He says "3" in a medium pitch (tone) at the house, but it is high pitched when played back at the facility; he says "8" in a medium pitch, and it's also high pitched later. And finally he says "9" in a low pitch and it's played back medium pitch. Also very obvious is the fact that Jonathan never says "1" or "7."
Visible crew/equipment: When Michael breaks into the car, after he drives off you can see a camera standing in the back seat in the car, and it's pretty clear it's a stunt man driving. (Helps to pause at 18:07.) (00:18:05)
Continuity mistake: During the scene when Michael is attempting to deceive Brennen into letting him and Nate go (from the time Brennen receives the picture message to when Brennen leaves), Brennen's necktie (right below the knot) changes from having a dimple to being flat, 6 or 7 times during the scene.
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