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 9 February 1969 for testing, and wasn't certified for commercial use until 30 December 1969. The first 747 didn't enter commercial service until January 1970.
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.
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.
In the Cryofreeze chamber, they pass by long forgotten celebrities, one of which is labeled "Gary Coleman", even though the frozen celebrity depicted inside the tube is obviously a statue of Jaleel White dressed in his Steve Urkel costume from Family Matters.
In Vegas, Vanessa says they have to keep up the "context" that they are a married couple. She should have said "pretext." Though such a "malaprop" would suit Austin's character, the obsessively grammatical Vanessa should know better.
While the purpose of the joke/reference is obvious, the pronunciation of "Alotta Fagina" is technically wrong. If she is actually Italian, as Number Two claims, her last name would be pronounced "fah-jee-nah", as the Italian "i" is always spoken "ee".
Dr. Evil's lair is in Nevada but at dinner, Scott tells a story about being town earlier and nobody spoke English, they only spoke French. It would have been impossible for him to be in Paris and fly to Vegas in time for dinner. Scott never at any points mentions that he left Vegas; there are numerous French restaurants and people in Vegas.
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.
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.)
When Austin first arrives in Las Vegas, he is driving a LHD E-Type Jaguar, painted as a Union Flag. When he and Vanessa later escape from Dr Evil's lair, the car has changed to LHD, with Vanessa driving.
When Austin and Vanessa have a glass of champagne in Vanessa's hotel suite, Vanessa is flirting with Austin while holding a champagne glass and drinking from it. One second later, when they drop on the bed, Vanessa's glass is gone without a trace.
When the Fembots are first introduced, they are wearing see-through jackets. There's then a close-up on one of the fembots, without a jacket, and in the next shot all three are wearing those jackets again.
As Austin enters the casino bathroom stall, he goes through the motions of pulling down his pants, but when he sits, his pants are still on. In the next stall, as the Texan looks down into Austin's stall, his pants are down around his ankles.
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.
Numerous military individuals' uniforms nametags give their rank and then their last name. Military nametags like this ONLY contain the last name, not the rank - as there are other symbols on their uniform representing rank.
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.
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.
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.
The military policeman at "British Makeshift Headquarters" wear the wrong badge on their caps and lapels. It resembles a Brunswick star style emblem used by UK civilian police forces rather than the Royal Military Police cap badge (a wreath with the letters E R in the middle). Also they shouldn't be wearing red slides on their epaulettes.
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.
The British soldiers that attack Dr. Evil's base wear red vests that British soldiers would never wear, especially on a combat mission. Also they wear Parachute Regiment badges on their (poorly shaped) berets but the berets are light red rather than the maroon colour used by the Paras.
Dr. Evil suggests trying to blackmail the Royal Family over Prince Charles'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.
While Dr. Evil is preparing Project Vulcan for launch, just before the warhead is armed there is a shot of the drill being lowered into place. Judging by the extra's accelerated movements, it is clearly discernible that the shot was sped up.
While Johnson Ritter is filling Cmdr. Gilmour in on the reappearance of Doctor Evil, shortly after Gilmour says "He's back," his side of the screen flickers and he "jumps" slightly, the result of what seems to be a bad cut or edit.
The goof items below may give away important plot points.
When Miss Kensington is introduced, Basil calls her one of their "top agents". At the end of the film when Miss Kensington and Austin are in their suite talking to Basil on the phone, Basil congratulates her on being made a "full agent" after her success in the Dr. Evil case.
During the bathroom drowning scene. Austin is holding Paddy between his legs, in such a way that Austin would be stuck with his pants wrapped around the toilet base. Immediately after the toilet flushes, Austin walks out without having freed himself.