Factual error: When Michael attempts to start the Charger, the starter just clicks, indicative of a dead battery or faulty starter. He checks his father's logbook and reads "spark plugs." Unless the cylinders are filled with an non-compressible liquid, there is no way that spark plugs are going to prevent the engine from cranking.
Factual error: When Fiona slips Michael a "key" during their kiss, Michael keeps it and no problem. In reality, all prisoners are searched thoroughly before returning to their cells. This includes a full oral search.
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