Continuity mistake: When Bond escapes from the Willard Whyte facility in the desert in the moon buggy, a car that is chasing him goes over a ridge and turns on its side, as the buggy speeds by. A wheel rolls back into the shot, all on its own. It doesn't belong to the car or the three-wheelers also chasing, but looks like it belongs to the buggy, which has its full complement of wheels all through the scene.
Plot hole: While it is essential to the story, there is a problem with apes in the space ship. While it is the one that took Taylor to the future, there is no way the chimps could have salvaged the ship from the water (plus there wasn't enough time for such a salvage operation. Kira and Cornelius were living in the ape city we see in "Beneath the Planet of the Apes" never mentioning to Brent that they found a spaceship he could travel back with). They didn't have the technology for such an operation, no diving suits, and chimps are scared of water. Also, the water would have destroyed the power systems of the ship when it sank. (00:00:25)
Continuity mistake: In the early scene when Harry walks across the street to confront the wounded robber on the street ("Did he fire six shots or only five?"), the shotgun used by the robber is lying several feet from the robber's hand, but when he reaches the robber, the camera shot shows the shotgun just a few inches from the robber's left hand. (00:13:00)
Continuity mistake: When the drug tester gets done with testing the heroin, he blows out the lit candle on the bottom. But when there is a far shot of him talking, the candle is still burning.
Continuity mistake: Vera gets onto her bus just after Stan and Jack have put spiders in the cab. She is wearing boots when she discovers the spiders, causing her to run into the back of the lorry. As she does so, it is evident that she is wearing shoes.
Factual error: At the end of the movie the 1970 Challenger R/T that is shown crashing into the bulldozers is actually a 1967 Chevrolet Camaro at the time of impact. It's visible for just a few frames, from behind at impact (before exploding) and later as it stands on its nose, after the fire is put out. Note the plain steel wheels, painted silver in the latter shot.
Continuity mistake: The scene where the two guys have Delores (Jean) tied down and are about to rape her you can see the microphone at their feet as they sit on the ground talking about it.
Continuity mistake: When the gang of bad guys ride to the ranch there are nine of them. When they leave, and throughout the rest of the movie there are only seven, despite only one being shot off his horse at the ranch. (00:15:15)
Revealing mistake: After Lansbury makes her clothes start to move, her nightgown attacks someone and you can notice the strings that make the gown move.
Visible crew/equipment: Very early on in the movie, Neville is happily driving around the deserted streets. Half way through this scene the camera shows us Neville's view out the front windscreen of the car. Ahead, moving cars can be seen crossing the intersection, obviously where the streets hadn't been blocked off for the filming of the movie.
Continuity mistake: Near the end of the race, the cars are clean and dirty in the same race lap.
Plot hole: The police Inspector recounts the murders, comparing them to the ten Biblical plagues of Egypt, and he states that in keeping with this theme Dr. Kitaj was killed by rats. First, Dr Kitaj dies in a plane crash. Okay, he was attacked by rats in flight but nobody would know that - his plane crashes in a huge, violent fireball and nobody would find any rat remains after that. Second, there was no plague of rats in ancient Egypt! (Go ahead, look it up). Even if the police had made the connection between the mysterious deaths and the ancient plagues they would not make the connection here.
Visible crew/equipment: When Bumpy hires Shaft to find his daughter, Bumpy gives Shaft an envelope with money, and when Shaft stands up you can see the bulge of the hidden microphone and wire at the front of Shaft's turtleneck sweater. When Bumpy leaves the office Shaft turns around and there's a bulge at the back of his waist, which is presumably the mic transmitter. (00:26:10)
Continuity mistake: Polly Browne is in her dressing room with a picture of Tony Brockhurst on her mirror. She starts to sing and picks the picture off the mirror. As we see a close-up in her hands it is a totally different picture of Tony. As she puts it back, the photo has reverted back to the original.
Factual error: Prime Minister Peter Stolypin is shown at the Romanov Tercentery, which marked 300 years of Romanov rule. Stolypin died in 1911, yet the Tercentenary was held in 1913. Also, Alexei's Spala incident happened in 1912, and was also shown after the Tercentenary.