Continuity mistake: At the end of the film, Bond chases Kahn following the battle at Octopussy's mansion. In the short time it takes to run to a nearby plane, it turns from pitch darkness to bright sunshine.
Factual error: At the East German / West German checkpoint, there is a level crossing. The warning signs for road traffic are clearly visible and are unique to the UK (where the shot was filmed).
Plot hole: When Bond is on the roof of the train ,he opens the roof panel on the rail car, jumps down into the car, and puts on a gorilla suit to hide. He does all this while the knife thrower is in the small car. Wouldn't the knife thrower have heard something? The roof panel opening alone would have amplified the train's noises, not to mention the air that would have blown in.
Factual error: Bond tells Q at one point "I've lost my PPK." However, he has been carrying a Walther P-5 throughout the movie, and continues to use it in the later action sequences. A PPK never does make an appearance in the movie. The P-5 was also used that year by Bond in "Never Say Never Again").
Revealing mistake: When the police cars chase Bond and stop outside the circus, you can clearly see a lot of brake-marks. It's quite obvious that the filmmakers re-shot the scene several times, before they got it right, but didn't bother to remove the marks made in earlier takes.
Factual error: During one of the chases, when James Bond hops into the water, he is picked up by a group of American tourists on a tour boat. The city of Cincinnati is misspelled as Cincinatti on it.
Revealing mistake: When Bond and Gobinda are fighting on top of the train, Gobinda rolls over with his sword, which bends like a rubber prop.
Factual error: On the railroad when the knife-thrower is welding the jewel canister onto the circus equipment, there are bright flashes of light. Later however, the knife-thrower attacks Bond with a gas welder. Oxyacetylene torches (gas) merely heat the metal until it melts. They do not produce blinding flashes, unlike arc and MIG welding kits (electric).
Revealing mistake: The nail-bed's steel nails that James Bond flips a henchman onto are the most obvious rubber nails ever seen in a film. They ALL move like crazy rubber in a bunch of separate directions when he falls onto them, including ones he never even comes close to touching.
Revealing mistake: In the scene where Bond is trying to escape with his new Mini-Jet, he flies through a big hall. If you look carefully, you can see that the aeroplane which is supposed to be flying with its wings vertical is fastened to some kind of sustainer.
Other mistake: When Bond drives into the train tunnel, below the train cart with the jewelry, we see that welding is going on in the other train cart. But that is before the bomb is placed in the hole below the cannon. There is no sign of weldings, and no sign of welding equipment once we get inside that cart.
Continuity mistake: When we see Q fishing, the lighting is totally different from when he's seen from the back in the next clip. Also the bank rises close behind him when seen from the front, but in the next clip the camera position is further back. Those are not shot in the same place.
Continuity mistake: When Bond's Mercedes is on the railroad tracks, it is hit head on by an oncoming train. As it is shown sailing in the air backwards, it is very clear that the drive-train has been removed. When the car is shown again, it is now sailing nose first as it hits the water.
Factual error: Being in Berlin talking about the Octopussy Circus, M says that Karl-Marx-Stadt (now again "Chemnitz") is further to the east, however it is 200 km to the south of Berlin.
Continuity mistake: When Bond is taking off with his Mini-Jet he nearly hits the jeeps and trucks that are chasing him. The landing gear is still down. After the cut you can see the scene from the other side and now the gear is suddenly up. There is no interruption between the two shots, not even the two or three seconds the gear takes to retract.
Factual error: Bond pulls his mini jet out of the path of the missile racing in from behind, making it narrowly miss his aircraft. Like most such piloting stunts from Hollywood, it wouldn't have worked. Modern anti-aircraft missiles have proximity fuses and fragmentation warheads or continuous-rod warheads. They actually deliberately pass by the aircraft they are trying to destroy and explode next to them, because the cross-section is greater that way. There have even been cases when a missile actually hitting an airplane just disintegrated without exploding, thus saving the target.