Plot hole: Necros had absolutely no way of knowing that Bond and Saunders had arranged to meet at the cafe when they did, and wouldn't have had anywhere near enough time to track them down and set up his elaborate booby trap. Saunders only suggested the meeting place and time a few hours earlier, and it was kept strictly between him and Bond. The scene in Tangier where Whittaker tells Necros to kill another British agent takes place on the same day Bond arrived in Vienna; meaning that Necros got from Tangier to Vienna (a 5 hour-plus flight), tracked down Saunders, acquired the materials to booby trap the cafe doors (or had planned this ahead of time - unlikely) and set the trap up well in advance of he and Bond getting to the fairground. There was nowhere near enough time for all of that to happen without Necros having psychic knowledge of Saunders' movements.
Continuity mistake: Dick Jones brags (admits?) to Robocop, "I had to kill Bob Morton because he made a mistake. Now, it's time to erase that mistake" while Robocop is crouched on the ground, not only looking away from him from across the room, but also Robocop's eyes are in a vertical position. In the playback, Jones is facing the camera as though it were videotaped or filmed in a studio. (01:10:50 - 01:35:10)
Factual error: At the end when the shark is attacking the boat and the electronic device is used you can hear the shark roar. Sharks cannot produce this sound since they have no vocal cords.
Continuity mistake: When Eliot Ness is at Jim Malone's house for the first time, Malone's collar is opened, then buttoned, then open again.
Revealing mistake: Riggs handcuffs himself to the depressed businessman. They jump off the building but they're not handcuffed to each other anymore. They used plastic cuffs which could separate during the stunt in case anything went wrong. They break just as they jump, so they grab each other's hands to stay in contact. After they land the cuffs are attached again. (00:31:00)
Plot hole: Explosions are very predicable and leave very clear traces after detonation, and the precise epicentre of a small nuclear explosion could be established within a few meters. Experts from the United States military could show that the nuclear explosion originated outside the airbase, and the evidence they could show (aerial photographs, etc) would be irrefutable. They could even invite their counterparts in the Russian military to see for themselves. The only way Petrofsky's plan could have worked would be if he could somehow get the bomb inside the perimeter of the airbase - not a terribly likely proposition.
Factual error: The Pentagon is the largest office building in the world. It has seven floors, 28 kilometers of corridors and 620,000 square metres of office floor space. The idea that the entire building could be searched in one afternoon by six people is beyond absurd. If those six people could search an average of one office every five minutes and they worked twenty four hours a day, seven days a week they'd get through the whole building in 89 days and 15 hours. I don't think the punter they are looking for has a lot to worry about.
Continuity mistake: When Corrine takes off her blouse, she shows her children seventeen scars on her back that she got from being whipped by the grandmother. Later in the movie, when Corrine is dancing at a party, she is wearing a strapless dress and there are no scars or any signs that she was struck with a whip.
Revealing mistake: Mac and Dillon go after the Predator. The Predator is sitting in a tree, and Mac points him out to Dillon. They both agree that they see it and take position. Mac crawls underneath the alien and is killed by his laser. The Predator then sees Dillon and lasers his arm off. Dillon's arm falls to the ground with the gun firing. Quickly Dillon turns and reaches for the machine gun around his neck. When he turns you clearly see his bloody right stump and his right arm sticking out the bottom of his jacket. [Note: As far as I can work out, this has been cunningly edited out of the UK DVD version].
Continuity mistake: In the opening scene, Gunnery Sgt. Hartman is making his speech and passes by Privates Cowboy and Joker on his way to the other side of the barracks. On his way he passes Private Pyle standing to the right of Private Joker. Later in the scene, when he rushes over to confront Private Joker and then moves on to Private Cowboy and then Private Pyle, Private Pyle is on the left of Private Joker. (00:02:00)
Continuity mistake: In the car chase scene, the escaped convict and police are exchanging gun fire between cars. In the different shots of the police car, the bullet holes in the windshield appear and disappear several times. Also, when three shots have been fired at the police car there are four bullet holes in the windshield.