Other mistake: After Dan visits his wife in the hospital, he goes to Alex's apartment. In the scene where he's chasing Alex and crashes into the glass door, shattering it, look closely at his face and you'll see it's not Michael Douglas but a stunt double. A few seconds later when they are struggling in the kitchen, look again and you'll see the same stunt double.
Other mistake: Dan and Alex go to what looks to be Alex's apartment after meeting at the office and going for a drink. After romping around in bed, they go dancing, and on the way back through the meat-packing district, she leads him to the door of her apartment and tells him she lives upstairs and he says something like, "this is your building?" It seems odd as they were just up there having sex.