Though they took the time to digitally add the World Trade Center to the final shot, they didn't edit out the Citigroup Center, Trump World Tower, and the Bloomberg building, which were built after the time of the movie.
When the first Palestinian target (the translator of 1001 Nights) turns at the corner at his house, right before his assassination (around the 37th minute of the movie) a modern parking meter is visible with a sign of a cellular phone.
The team meets in an underground room to debrief the team leader. Along the far wall, behind the reel-to-reel tape recorder, is a water cooler with a
polycarbonate bottle. At the time, water coolers had glass bottles.
The term "honey trap," which is used in the film, was first coined by John LeCarre in 1974 (publication of Tinker Tailor), so it's very unlikely (we don't have the exact time line of that incident in the movie, or indications of reading habits) that it would have been used.
The black Mercedes W114 230.6 used by the KGB agents during the Greece assassination scene is patched together to make it more "historic." The front doors were made to look like a Series 1 model, with divided side windows, made prior August 1973. The side mirror was removed completely. The rest of the car is clearly a Series 2 (post August 1973), including the model designation 230.6 itself (it should read just "230", the two different models 230.4 and 230.6 co-existed after August 1973).
When Avner is leaving his apartment in New York, a yellow "rubber bumper" MGB is present in the line of cars on the side of the street. The federally mandated rubber energy absorption bumpers were not installed on MGBs until late summer of 1974 as a 1974/5 model. The age of Avner's daughter would seem to suggest this scene takes place sometime before then.
When walking on the waterfront in Tel Aviv, a rusty beat-up 1972-79 VW Bus appears on the street. The scene takes place in late 1972. A brand-new first year model would not be that beat up and rusty after just a few months.
When Avner is waiting for the Palestinian's daughter and wife to come out of their building, before letting off the telephone bomb, the little girl says the same line twice. Off-screen, she says hello to her driver before she actually meets him. She comes out, repeats the same line, and says hello to the driver when she meets him.
In Greece, just before the large explosion, Avner, who is supposed to be fluent in German, asks "Kann ich ein Licht haben?" as he asks for a light for his cigarette. The person responds "sind Sie Deutscher?" ("Are you German?"). The correct question is, "Kann ich Feuer haben?"
When Eric Bana as Avner is speaking to his wife on the phone, his wife tells him he should hear "her" referring to his daughter. He immediately says, "can he hear me?". Realizing he made a mistake, he then says "can she hear me?"
Steve and an Italian girl observe the first target in Rome from an Alfa Romeo Giulia (model 1974 or later, with a straight trunk). When the target walks through the street, putting on his coat, Steve and the girl drive away in a Lancia Flavia. When the target is in the store, they arrive in the Alfa Romeo Giulia.
When Avner walks into Papa's home, he walks towards the kitchen past a table. There is a man standing next to the table talking to someone sitting down but in the next shot, the man standing up is gone.
When the team is eating dinner after the assassination where Avner is nearly blown up in the adjoining room, the scene begins with a white rug under the table and then the rug is mystically gone in the later scene and bare wood floors are seen.
At the shootout at the airport at the end of the movie one of the terrorists machine guns the first group of hostages in the first helicopter, throws a grenade into it, and takes off running. In the wide shot of the helicopters when it shows the one on the left exploding, you can see the terrorist who threw the grenade running to the other helicopter and his body is hit with several bullets. In the next scene, that same terrorist is running toward the camera and again he gets hit by the bullets.
Just before the terrorist with the cowboy hat (Tony), shoots one of the athletes through the cheek, we see a terrorist in a denim jacket and beige ski mask looking on in the background. As the shot goes to a different angle we see a different terrorist in a yellow shirt threatening an athlete (out of shot).
When Avner and Louis are leaving Papa's house after their meeting, they are both seen entering the back seats of the car and sitting down. But in the next shot only Avner can be seen in the back of the car.
When Avner meets Andreas and his friend Tony in a Rome café, there is a huge statue of Queen Victoria, in her extremely distinctive pose, in the middle of the square, with the British coat of arms on the pedestal, betraying the location as Malta.
When Avner and Ephraim are walking along the beach in Tel Aviv, the sea is to the left and the sun is casting shadows towards the camera, revealing that they are walking north. The scene must have been shot on the east coast of Malta, not in Tel Aviv, on Israel's west coast.
In the film, the German snipers at the airport were using rifles with telescopic sights. In reality, the Germans were criticized for their lack of preparation, including the fact that none of the snipers had telescopic or infrared sights.
When Carl goes into the apartment building lobby to "sweep" the scene of the first assassination, he picks up a spent shell casing that is clearly a .22 Caliber shell. The assassins were both armed with Beretta M1951 model pistols, which fire 9mm. (Interestingly, the actual assassins in real life likely used Beretta Model 70s, which do fire .22 Caliber.)
Late in the film Avner makes a telephone call from a booth on a street apparently in Brooklyn. He gives the phone's area code as 212. This was correct at the time the movie was set - Brooklyn changed to the 718 area code in 1984.
At the beginning of the movie, the Munich Olympic kidnappings are on TV. Actors are watching the footage on screen as if it was happening live, but the date of the events is displayed on the ABC news coverage. The news footage is clearly archive footage.
Just before the credits roll, Avner asks probing questions of Ephraim. They are in a small park on the north end of Gantry Plaza State Park, near 48th. Ave. & Center Blvd., just north of Avalon Riverview, Queens West, Long Island City. SSE across the East River are the high-rises of Peter Cooper Village behind Avner and to his left (our right), and the low-rises of Stuyvesant Town directly behind him. The World Trade Center towers have not been digitally added to these shots - "Break bread with me, Ephraim" - but have been added to the pullback about a minute later.