Revealing mistake: During the bedroom scene with Felicity and Fat Bastard you can clearly see the air hose that fills his suit when he rolls over in the bed. (00:49:10)
Continuity mistake: When Austin is about to be sent back in time in the Bug, he reverses into some shelves with computers on them, knocking them over. He then pulls forwards. When he reverses again, the computers are back up, and he hits some barrels. When he pulls forwards again, the barrels are back up, but the computers have now disappeared again. (00:23:50)
Continuity mistake: When Fat Bastard falls down at the end, he disappears once the dancers come in.
Continuity mistake: In the scene when Mini Me and Young Number 2 grab for the cookies, when Young Number 2 grabs there are two, one that looks like chocolate chip, and a plain one. When Mini Me grabs for it there is just one. (00:52:35)
Continuity mistake: When Mini Me and Austin are fighting on the moon Mini Me bites Austin's spacesuit and you can see his British flag underwear. But after he sends Mini Me out into space, he drops the space suit and Austin is now wearing a blue jumper with no holes in it. (01:17:25 - 01:18:20)
Revealing mistake: In the scene where Mini Me is drawing the goodbye card to Scott, (before they go to the moon) you can see that the drawing is already on the page and Mini Me just traces it over. (01:05:50)
Continuity mistake: During the scene in which Mini Me draws the "goodbye card" to Scott, (which, as explained already on the list was drawn ahead of time), there seems to be a red spot under Scott's body on the paper, no doubt signifying blood. But where did he get the red marker to draw it? (01:05:50)
Continuity mistake: At the end of the movie when Fat Bastard comes in Austin's room he breaks the door and pieces fall on the floor but later when you see the door the pieces aren't there.
Continuity mistake: Part of the time Doctor Evil's eyes are blue, part of the time they are brown. Specifically when he's talking to the President in 1969.
Continuity mistake: When Austin and Felicity are having a fun time in London, they stop and sit down at a table. Shortly after they sit down there is a lady behind Felicity in yellow and orange. Then it cuts to Austin, and she's behind him as well! There is no way someone could move that fast. Originally I thought that was the waitress outfit, so there could be more than one, but it's definitely the same woman both times, and on wider shots we only ever see one woman.
Continuity mistake: In the scene where we first meet Mini Me at certain points, if you look closely, the bottle in front of Scott is 3/4 full then suddenly empty.
Continuity mistake: In the scene where Felicity shoots out Mustafa's tire, you can see in the next two shots that the tire is fully inflated as it goes off the cliff.
Deliberate mistake: When Austin and Felicity cross the street when they are shopping, you can see green hills behind them, very much like Hollywood and not 1969 London. (Deliberate reference to an earlier joke)
Audio problem: Towards the end, when Felicity Shagwell is captured in that glass tube, there's a shot of the entire room and she is yelling for Austin Powers but her lips aren't moving.
Continuity mistake: During Elvis Costello and Burt Bacharach's number, the drummer's snare rim taps are not in time with the actual music.
Continuity mistake: After the assassin throws the knife into Robin Swallows' back, the shot cuts to the assassin. But when it cuts back, Austin is looking quizzically at her back, and we see why. The knife has disappeared! But in all subsequent shots (except when she falls and hits the ground) it is there. (00:27:45)
Continuity mistake: When Fat Bastard explodes through Austin Powers' bedroom door, you can see where his right arm was meant to break through, but didn't. The piece of the door is shown still intact for a moment or two, but with the outline of his arm surrounding it. It disappears in the very next shot of the door only a second later.
Continuity mistake: At the start the astronaut is working on the satellite and turns around fully, then stops and sees Big Boy. The camera changes angle and the astronaut is still turning around.
Continuity mistake: In the scene where Austin and Felicity are downtown on the sidewalk, they alternate long and closeup camera shots from the same angle. There is a crowd of people standing around watching them in the background on the long shots, but only individuals walking past, ignoring them, in the closeup shots.
Visible crew/equipment: In the scene where Felicity and Fat Bastard are in bed together, a certain shot reveals that under Fat Bastard's breast is a patch of velcro which holds it down.
Answer: It's called "Soul Bossa Nova", by Quincy Jones.
Grumpy Scot