Continuity mistake: Michael is having a meeting with the guy who is asking how Michael found out about him (where Sam is standing guard with the sniper rifle.) Michael has a gun pulled on him and is trying to escape. As Michael is trying to leave in the Charger, he pulls backwards and makes a 90 degree turn so that the passenger side of the Charger is facing the guy with the gun. The windshield could not have been shot from this angle. The next camera shot Michael is driving backwards again with the windshield facing the guy so he can shoot a hole in the center of Michael's windshield.
Continuity mistake: When the heroin importer is questioning Sam, he has his hand around his face, with his fingers touching his ear. When the shot moves to the front, his hand is more on his throat and nowhere near his ear. When we cut to the back, his hand moves again.
Continuity mistake: When Michael is on the phone with the heroin dealer at the docks, he has his phone at his left ear. When the camera moves to a shot from the back, there's no phone near his face (or in the frame for that matter) and his mouth doesn't move while talking. When the shot cuts back, the phone instantly is back at his ear.
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