Cady asks Bowden to recite Canon Seven of the ABA Model Code.
The Model Code was abandoned in 1983 and replaced with the Modern Rules of Professional Conduct, which has no canons. As Cady had been in prison for 14 years, the earlier Model Code would still have been in place when Bowden represented him.
When Sam Bowden is first confronted by Max in his car, he offers to buy Max off. Max counters Sam's hypothetical $10,000 offer with, "Let's say $50,000--$50,000 into [about] 5,000 days" equals $10 per day. He meant to say 5,000 days into $50,000, which would give his daily pay rate. (The first calculation equals 1/10th of a day per dollar.)
At the start of the scene where the hired goons attack Max in the parking lot, Max is wearing his watch when he turns to face them after one of them calls his name. About half way through the scene Max's watch inexplicably disappears from his wrist.
When Cady is kissing Danielle, he leans to the right. When the camera switches, showing the back of Danielle's head, now Cady is leaning to the left. This sequence happens again when the camera switches back to its original angle.
When Danielle and Max are talking in the theater, she tells
Max that part of her punishment for smoking grass is that she can't drive the Cherokee. Their model Jeep is a Wagoneer, although it was a package on the Cherokee model.
When the private eye is waiting for Cady in the house, he finally sees Teddy Bear moving, and follows the wire to the windows which (looking from inside) have closed shades. In very next shot, from outside, he is walking up to this window to close it, but there are no shades on it at all.
Before retiring for the night, the Bowden family and investigator Kersek securely close and lock all the doors and windows in the Bowden home. Yet a short while later, the wind blows one of the doors open.
When investigator Kersek is crawling along the floor in the Bowden house following the fishing line that is moving, you can see that there are no bullets in the cylinders of his revolver. It is true that perhaps he only had a bullet in the chamber, but it would be more likely that under the circumstances that the gun be fully loaded.
At the end of the film, Sam Bowden says that he had to go to hearings before the American Bar Association as a result of his criminal actions toward Cady. But the ABA doesn't license lawyers, nor does it have the authority to disbar them. It is a lobbying group. Bowden would have had to go before the Georgia Bar Association, given that the crime occurred in that state.
Even at the time this movie was made, there were already stalking laws in all states across the country, which read that "any person who willfully, maliciously, and repeatedly follows or harasses another person, and makes a credible threat with the intent to place that person in reasonable fear of death or bodily injury, commits the offense of aggravated stalking." Thus, Sam could have easily had Cady arrested and sent back to prison, precluding everything else that followed.
Max Cady tapes Sam's threat to do the "hospital job," and then uses that tape recording in court to get a restraining order against Sam. Although Sam admitted making the threats, no tape recording in any state in any court of law is admissible as evidence.
As the Bowdens drive towards Cape Fear, a sign for "Cape Fear..Next exit" is reflected in shimmering water. The words can be read normally, whereas reflections of text in water would have to have the text up-side-down.
Sam orders the "hospital job" against Max Cady in the hope that Cady will leave the Bowden family alone afterwards. During the actual attack, Cady takes eighteen repeated heavy blows with metal pipes all over his body and then stands up to fight back, a complete impossibility. Max Cady would have been dead.
When Kersek walks into the kitchen before he's killed, we see Graciella's face and hear her speak. When she is out of frame, it's not enough time for Cady to kill her, switch clothes with her and come back from the pantry to the kitchen.