Continuity mistake: When the security guard comes back with the orange sherbet, he hands it to Austin who takes it from him. But a few seconds later, when Austin and Vanessa are escaping from the destructing lair, neither Austin or Vanessa have the sherbet with them. [Just a note regarding this scene, the international version of the film contains this scene but not the US version. I believe it is a deleted scene on the US version of the DVD.]
Continuity mistake: This mistake takes place when Austin, Vanessa, and the guard are with the mutated sea bass. When Austin judo chops the tooth paste onto the guards face, the guard is wearing a helmet and half of it has toothpaste on the front. Then the camera does a close up on Austin. When it shows the guard again, he doesn't have his helmet on and half of his forehead has toothpaste instead of his helmet.
Continuity mistake: Watch the distance between Austin and Basil Exposition just as their first meeting comes to a close. It changes from far to near and back to far in the space of a couple of shots!
Continuity mistake: Near the end when Christian Slater comes back with the orange sherbert Austin has no gun, and then in the next shot Austin has a gun but no sherbert. [There are two versions of the film - a US, and non-US version. Christian Slater appears in the non-US version in a cameo role for a couple of lines.]
Continuity mistake: When the Vulcan drill is shown being rotated, first of all, it's being rotated in the wrong direction - in the direction that would make the drill face upward. Of course they could be planning to make a 360, but why? Also, if you look closely at the people below and around the drill, you'll notice that shot is in accelerated pace - everyone is moving really fast, like in old silent films. The guys in front of the drill are looking back and forth from their pads and the drill extremely fast. I guess it was done to show the drill rotation nicer.
Audio problem: When Austin and Mrs. Kensington are shooting at Dr. Evil after he gets into his Cryogenic Freezing Chamber, in the last shot before it shows the Big Boy shooting off of the club, many sounds of gunfire are heard, however, both Austin and Mrs. Kensington have appeared to have stopped shooting. (00:06:25)
Factual error: The 1960s London policeman at the beginning is carrying a baton on his belt. British police officers didn't start carrying batons until the 1990s. Before that they only carried short truncheons in concealed pockets. (00:01:50)