Continuity mistake: When De Niro first meets Nolte's lady-friend, they are having a conversation in a bar or restaurant. As the camera goes from De Niro to the woman, the woman's top blouse button is open in one shot, then closed, then open, etc.
Continuity mistake: When Sam is talking to the P.I about "Taking care of Max," he gets into his car and the window is up. A few seconds later, the window is down. There wasn't enough time for him to roll it down. (00:54:50)
Continuity mistake: When Max Cady calls Dani on the phone imitating her Drama teacher, Dani takes out her retainer and places it on the bedside table. After that, her retainer keeps jumping from the bedside table to back in her mouth for the next several minutes until she finally puts it back in when she hangs the phone up.
Plot hole: Cady's plan to get revenge on Bowden includes raping and assaulting Lori. This part of the plan, however, hinges on Lori not reporting Cady to the police, which he had no way of knowing that she wouldn't. If she reported him, the investigation would have created huge problems for Cady. He bit off a chunk of her face, so the wound could have been matched to his teeth, as well the chunk of skin he bit off and spit out most likely would have had traces of his saliva on it. Not to mention evidence that could have been gathered from a rape kit and eyewitnesses that could have placed Cady at the bar with Lori beforehand (the bartender, for example). In all likelihood, he would have been arrested, tried and convicted. Lucky for him, Lori was too ashamed to report the incident.