Continuity mistake: Near the beginning of the film in the bar scene, we see Joe and Jimmy Dix talking then, Jimmy throws a punch and Joe catches it, knocks Jimmy down and he walks off. If you slow this part down as Joe begins to sit down again, there is a glass on the table half full with scotch, then when Joe reaches for the glass it is turned over and spilt, as he says, "Spilt my warm cup of piss ". (00:23:50)
Continuity mistake: When Wayans and Willis are chasing the limo on the freeway, Wayans draws a picture of a bomb to hold up to the guys in the limo. He draws a large circle with about 6 lines coming out of it with the word "BOM" underneath it. When he holds the picture up at the window, there is only 1 line radiating from the circle. (01:20:40)
Suggested correction: The same drawing is used, the top is slightly cropped but the lines are still visible.
It's not the same picture. In the scene (not screenshot), the top isn't cropped and you see there're fewer lines, and the circle is different. Not only that, but we see in the car "BOM" is written differently than what we see when it's against the window. Also, when he first draws the bomb, the holes in the paper are on the left, but against the window they're on the right. One could argue he flipped the page over to start again, but we already know the final drawing is different.
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.