In the edited television version, Alotta Fagina's name is changed to Alotta Cleavagé. Yet in Dr. Evil's lair, after Austin and Vanessa are captured, you can clearly see a switch labeled Alotta Fagina. (Although this error was on the part of the network censors rather than the filmmakers.)
The briefcase Number 2 sets on the table when he offers Austin the business proposition is closed in one shot, and appears open and full of money in the next. This is due to a cut scene which is shown after the movie on the video release, but appears as a continuity error in the actual movie.
For most of the movie, Dr. Evil's eyes are blue, but in some shots, they are brown.
When Austin is brought back to the present, two women take a clip off each ear, but they reappear.
When Austin Powers knocks out the woman in the party at the beginning, her hat gets knocked off, but when Austin grabs her/him, the hat is back on.
The Marching Band featured on the opening London scene is an American high school style band not British. The give-away is that American bands tend to use Mellophones instead of French Horns, Trumpets instead of Cornets, Marching Baritones instead of upright Baritones, and Sousaphones instead of regular tubas. Also as Mike Meyers notes in the DVD commentary, civilian marching bands like this aren't really a thing in England, except for colliery brass bands in northern mining towns.
Numerous military individuals' uniforms name tags give their rank and their last name. Military name tags like this only contain the last name and not the rank. There are other symbols on their uniform representing rank.
In the opening dance scenes in the street, an extra on the left hand side is holding and waving a Union Flag which is upside-down.
In the swinging London title sequence a Beefeater stands on a street corner. Beefeaters (or Yeomen Warders) are only found at the Tower of London, they aren't stationed around other areas like bearskin-wearing guards.
Number Two says that Virtucon owns cable companies in 38 states. But on the map, only 36 states are highlighted (at the most); even if Hawaii (which isn't shown) is one of them, the total is only 37.
Dr. Evil suggests trying to blackmail the Royal Family over King Charles III's affair, not knowing it's already become public and he and Princess Diana divorced, except he didn't marry her until 1981 and Dr. Evil was frozen at the time, and when trying to resist the fembot, Austin thinks of Margaret Thatcher, who wasn't well known to the general public in the 1960s. But both of them took crash courses on the intervening years; while clearly incomplete, they may have included this information.
When Random Task throws the shoe at the small bust, it's quite obvious that it's a rather thin/hollow bust, making it quite easy to break. This is an homage to the same goof in Goldfinger (1964).
It's never made clear how Random Task knew where Austin and Vanessa were having their honeymoon towards the end of the film, especially when you consider it's been months since Austin defeated Dr. Evil. Vanessa is revealed in the sequel to be (or have been replaced by) a Fembot. She may have had a tracking device in her body.
Vanessa reveals she has dental floss on her when she and Austin are placed in the sea bass trap. It should have been confiscated by Dr. Evil's guards when the two were captured. Dr. Evil's running incompetence is an ongoing theme throughout the series (he even says he's closing the doors and assuming everything is going according to his plan).
Austin pulls out several cigarettes and a lighter during his dance to destroy the Fembots. Where'd he get them from? He couldn't have possibly had them on him after he and Vanessa were captured as Dr. Evil's guards would have confiscated anything they had on them. Dr. Evil's incompetence is a running gag throughout the series. A blunder like this certainly isn't out of character for Dr. Evil, who needlessly complicates his plans or thinks everything will go the way he wants it to.
Albeit easy to miss, Austin is seen wearing nude-colored briefs when he enters the hot tub with Alotta.
During the honeymoon sequence at the end of the movie, there's a red duct tape covering Vanessa's nipple behind the flowers while she talks to Basil.
When Vanessa is talking to her mother on the phone, it is obvious that she is watching herself on a screen out of frame in order to line up the objects she is holding with Austin.
During the final "nude" scene with Austin and Vanessa, Austin rises slightly off of the sofa, and some kind of underwear is revealed.
In some places Austin isn't wearing his teeth, most noticeably during the scene with Alotta and her hot tub.
Commander Gilmour's aide Philips wears the rank insignia of Senior Airman but his name badge reads "Sergeant Philips."
Gilmour wears the uniform of a U.S. Air Force 4 star General but is addressed as "Commander Gilmour." Although he is the head of U.S. Strategic Command and the title of this position is Commander, according to convention he should be addressed as "General Gilmour." "Commander Gilmour" implies he is a lower ranking naval officer.
Austin's Jaguar E-Type (which first appears in London at the start of the film) has no front numberplate, this is illegal in Britain.
The gold leafs on the Russian General's lapels are the wrong design and are pointing upside down.
In the title sequence there's an "UNDERGROUND" sign on a wall, but it's missing the red roundel that London Underground street signs have. It's also a bit too large and there doesn't appear to be a station entrance anywhere in sight.
In the opening sequence, a British policeman is shown with a nightstick and wearing a helmet with riot straps. In 1967, a police officer would have only been issued with a truncheon (a 12 inch long piece of wood). The helmet riot straps were not introduced until the 1980s. In both cases, the normal uniform would not have either of these items showing.
Austin Powers' personal aircraft is said to have been stored for him when he was frozen in 1967. The aircraft in question is a Boeing 747, which first flew on February 9, 1969 for testing, and wasn't certified for commercial use until December 30, 1969. The first 747 didn't enter commercial service until January 1970.
When Vanessa briefs the British soldiers they are both holding SLR rifles. By 1997 the SA-80 (or L-85A1) rifle had replaced the SLR.
The plane in the movie was leased from Qantas Australia, registration VH-EBV, a 747-238B. First flying in 1971, it cannot possibly be Austin Powers' personal aircraft. EDIT: This is akin to saying that Austin Powers or Dr. Evil never existed in 1967. The movie is likely using a slightly alternate history in which the 747 aircraft in question was in service at an earlier point in time to our reality. Many other elements of the film do not exist, such as the Republic of Kreplachistan. So clearly, the film isn't functioning in an exact mirror of our reality. But even if it is meant to be, isn't it also possible that Austin Powers, as a secret agent of the British Ministry of Defense, could have had early access to a 747 prototype in 1967 that was later used by Qantas after Powers was cryogenically frozen? The registration could have been altered or added at a later date.
When Austin is dancing down a 1967 London street, some of the street corners have modern curb cuts. They are hardly going to redo every single curb and corner.
When Austin Powers and Mrs. Kensington are shooting at the cryogenic freezing chamber which Dr. Evil has entered, the last two shots are heard, but the guns are not shooting anymore.
After Austin has been unfrozen and is about to meet Vanessa Kensington, he looks at two nurses who help him up. The audio of him saying "Hello, Hellooo." can be heard, but Austin's mouth remains closed.
When Austin breaks into Alotta Fagina's penthouse apartment, he is taking pictures of Virtucon's plans with a miniature Hit camera. It sounds like there is a motor drive advancing the film, but Hit cameras were not so equipped.
When Basil video calls Austin, at one point he tells him he is to be knighted. Austin replies "that's very shagadelic" but his mouth does not move.
When Austin is urinating following his being unfrozen, you can hear the sound effect of him doing so, but there is no stream of urine visible.
During the scene where Austin and Vanessa swing off the mechanism with dental floss, a supportive harness is connected to the floss.
After Cmdr Gilmour arrives in London, a caption is displayed on screen, 'Ministry of Defense,' the American spelling. In the UK, the MOD is spelled 'Ministry of Defence.'
In the opening musical sequence, supposedly set in London, several of the parked cars seen in the background are clearly US-specification models, revealing the fact that it was shot in America. A Rover 2000 sedan is seen with three scoops on the bonnet/hood (only US-market cars have these) and an MGB GT is seen with extra-large US-spec side marker lights.
Bolton (the tour guide at Virtucon) states that the company makes volatile chemicals, although Number 2 had stated earlier that Virtucon abandoned this industry in favor of communications.
When Austin is going through the names of people from 1967 who dies, he lists Janis Joplin's cause of death as alcohol. Joplin actually died from a heroin overdose.
When Austin (who is supposedly British) pretends to Vanessa that he's "taking the elevator," he uses the American term for it as is, rather than the British term "lift."
In the movie commentary Mike Myers admitted they didn't realize that the band that Austin leads during the musical sequence is an American marching band. These are uncommon in England.
While playing BlackJack with Number 2, cards are dealt to Number 2, Austin Powers and the Dealer. Number 2 takes a hit on his 17 after using his eye-patch x-ray to determine that the next card is a 4. Then the dealer deals Austin his second card to show his 5, which he stands on. In BlackJack all players receive their 2 cards and then are allowed to hit or stand, in this instance Number 2 took his hit card before Austin had been dealt his second card.