Plot hole: When the police chief asks Joe 'where's the briefcase they were telling me about?' Joe tells him to look in the back seat of the white BMW. There are a couple of problems with this. First, the police chief is looking for a case with a bomb in it, because he received a phone call from the guy who had his BMW stolen. Even if he knew about the money, which is unlikely, the police chief has no way of knowing that the case he is about to open is not a bomb, since no-one saw Marcone steal the case with the bomb in it. Yet he opens it without calling the bomb squad. Second, Joe saw Jimmy put the case with the bomb in the back seat, so why doesn't he warn the police chief about it? (01:35:00)
Plot hole: Mike already knows that Joe is back in town from Vegas because he spoke to him at his office after initially saying he was going to leave a message. He didn't inform Joe's wife because she asks him when he comes home. And Mike was at Joe's house when they talked because he has on the same robe when he steps out the closet from hiding. Why wouldn't he have already left if he knew Joe was back in town?
Suggested correction: Mike didn't think Joe was going to come home, especially if Joe was back in town but at his office. Plus, Joe told Mike he'd meet him at Mike's office in an hour. So, Mike took a shower to get ready. Making a bad decision, when you're in the middle of the poor decision to sleep with your friend's wife, isn't a plot hole.