Factual error: It's mentioned that the British and New Zealanders turned the Americans away. This is untrue - the Americans stayed with both for a time until it was decided that they would be safer with the Canadians.
Factual error: The Canadian military policeman (Sgt. Claude Gauthier - based on a real person) depicted as the house guests leave Ken Taylor's residence, and subsequently shown breaking up communication equipment has several errors in depiction. He is shown wearing combat uniform while on diplomatic duty (although perhaps the situation excuses this). He has service dress sergeant's chevrons sewn on the arm of his combat uniform instead of combat uniform rank. He is wearing a military police red beret, but at that time Canadian military police wore green berets. Also, having enough years of service to attain the rank of sergeant, he would have known how to form his beret properly, rather than having it look like a pizza. The slip ons worn on his shoulder epaulets are way too long, and are not like any Canadian Armed Forces slip ons for any uniform. They are definitely not Canadian combat uniform slip ons. The chest pockets on the combat shirt are sewn flat, whereas in reality the chest pockets had sides (they stuck out from the shirt) as they were designed to hold ammunition magazines for the FNC1 rifle. The buttons on the chest pockets are small, like the ones running down the front of the shirt - the pocket buttons should be much larger in diameter than the shirt front buttons, His long hair and sideburns would not have been permitted under the dress and deportment regulations of the Canadian Forces, and as a Sergeant he should have known better.
Factual error: At the end of the movie a large Boba Fett action figure is shown on the shelf. The only Boba Fett toys available before "The Empire Strikes Back" was released in 1980 were small action figures sent as a free gift promotion to people who had collected enough "proof of purchase" tokens for purchasing enough other "Star Wars" action figures from the Kenner toy company.
Continuity mistake: Ben Affleck gets into a 280s Mercedes driven by the Canadian Ambassador. The front screen wipers on the car are original silver chrome style and fit the screen. When they arrive at his house the wipers have now changed to much shorter modern style wipers, are black, and are the very latest frameless style first introduced in the early 2000's by Bosch.
Factual error: In the scene where the Swissair 747 is taking off from Tehran the police cars keep up with the plane until it lifts off. Takeoff speed for a 747 is about 160 mph so the police cars would have been far behind by then.
Continuity mistake: When the State Department approves the exfiltration, Ben Affleck is dropped at Dulles Airport (it has a distinctive swooping roof), but after he boards, the plane is seen taking off from Reagan National airport. The evidence is the fact that you see a bridge (the Woodrow Wilson bridge, which was rebuilt in 2006 and can be seen in its current form) in the background.
Continuity mistake: There is a scene after Tony came up with the idea for the fake movie and presented it to the CIA, where he is looking at papers under a magnifying glass. Tony is holding his cigarette in his left hand under the magnifying glass. The very next shot shows his face, and he suddenly has the cigarette in his mouth. Which he then removes with his right hand. The next shot shows it in his left hand again.
Factual error: Iranian revolutionary guards didn't have caps with their uniforms until 1988 (after the end of the Iran-Iraq war).
Factual error: The embassy takeover was November 3rd. A scene in Washington DC described as 69 days later showed Tony Mendez driving around town with yellow/fall like leaves on the trees, something that would not have been true in the middle of January. A similar scene at the end of the movie has Tony Mendez approaching his house in Virginia and a very fall like scene is shown.
Factual error: In 1980 the Canadian airport we see was called Dorval international airport, not Trudeau.
Factual error: The turbans worn in the scenes in Tehran are not the sort worn by Iranian clergy - they are wound incorrectly and are too flat.
Factual error: They play a track "When the Levee Breaks" from a Led Zeppelin album. The hand shows the needle being placed at the next to last track on the album. However, "When the Levee breaks" is the last track on Led Zeppelin IV's second side.
Factual error: As a newspaper from January of 1980 is displayed, the Rolling Stones song "Little T&A" is played. That song appeared on the "Tattoo You" album, which was not released until Aug. 24, 1981.