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)
Revealing mistake: When the younger Bowden sprays lighter fluid into Max Cady's face, and he is on fire, for a few of the shots, Max Cady has no head. (01:51:00 - 01:52:00)
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 Nick Nolte confronts his daughter in her bedroom about meeting with Robert De Niro, as the camera angle switches from Nolte's face to his daughter's face, his hand over her mouth changes positions.
Continuity mistake: When De Niro kisses Juliette Lewis, the positions of their heads reverse twice as the camera angle changes.
Continuity mistake: When the Bowdens are eating dinner on their boat at Cape Fear, the wine glass that Lee is holding changes position and her grip on the glass changes throughout shots.
Visible crew/equipment: When Robert De Niro is smoking a cigar at the cinema, you can quite clearly see someone puffing and blowing cigar smoke from behind his seat to give the appearance of lots of hazy smoke.
Audio problem: When Claude Kersek is garroted by Max Cady, the 'strangling' sound effect is heard right before the piano wire goes around his neck, and then again when it does.
Continuity mistake: When Sam Bowden is talking to Max Cady at the restaurant, Max is secretly taping the conversation. When it is played back in the courtroom after Max's beating, how the conversation is delivered and some of the words differ from what was said before.
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.
Factual error: 'Cape Fear' is based in North Carolina, and cars shown in the film have North Carolina license plates. However, the cars have plates on both the front and back, and in North Carolina, cars only have plates on the back.
Continuity mistake: When Max is sinking at the end, there is the pole he's handcuffed to behind him which disappears between shots.
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.
Suggested correction: Luck didn't come into it. Cady specifically targeted her because of her connection to Bowden, and took the calculated risk that she would not want her sexual history being dragged in front of a court and all her co-workers. This ties into Cady's motive for wanting revenge on Bowden in the first place, as he had suppressed similar evidence in Cady's original case. Also, Cady is a very unhinged individual; the submitter's opinion on how sensible his actions are does not make them a plot hole.
Phaneron's point is valid. It's quite plausible that Lori would've been willing to testify. She didn't because if she did, the movie would've ended there. It's artistic license.
Visible crew/equipment: The girls jump off the house boat, leaving Max and Sam on board, as Sam tries to jump off Max grabs him, there are apparently sprays of river water but the hose creating the effect is visible.
Continuity mistake: After Max Cady killed Kersek and Sam Bowden finds his corpse in the kitchen, the blood pool changes shape in two different cuts.
