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).
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: 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.
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.
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.
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.
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.
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.
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.
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.
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.
Continuity mistake: When Bond is fighting the twin on the top of the train, there is a carriage behind them, but when both of them fall off the train, the carriage has suddenly disappeared.
Continuity mistake: In the final scene on the plane, Roger Moore and Maude Adams jump from the plane over the cliff. Moore grabs a crack in the rock. The next overhead shot his hand is by his head. Next shot it is in the crack again.
Continuity mistake: When we see the Monsoon Palace from the lake, it is set very high on a barren brown mountain. But when Bond escapes on foot, he very quickly is in a dense and moist jungle - and walking out in a low-lying march land with a wide river. That can't be the same lake, since we don't see him running down a steep barren cliff-side.
Revealing mistake: When Gobina first slashes at Bond during the climactic fight on the plane, a subsequent medium shot reveals a stunt double (note the bald spot). He's even wearing completely different clothing - a black stunt suit instead of a blue jacket and white shirt.