Continuity mistake: When Shirley walks through the door you can see over Alan's shoulder that he's reading the comics in the daily paper. As they talk the paper changes to the business section.
Other mistake: As Denny asks "did she sleep in your room?" Alan leaves Denny's hotel room, pulling the door behind him. The swinging door catch is in the closed position, sticking out from the door frame which would prevent the door from being able to shut - the shot cuts a fraction before impact and we hear the sound of the door closing anyway.