The action starts in 1963, in the day when President Kennedy was killed. The ambulance that brings Salomon Tauber's body to the hospital is a Volkswagen Kombi model 1967 or newer. The 1963 model had a split windshield.
During the final showdown between Miller and Roschman, Voight is wearing a black double-breasted raincoat, and Schell a white shirt, with exaggerated points. Both highly fashionable in 1974, but definitely not period wear for the early 1960's.
When Peter Miller phones his girlfriend from Munich Central station, there is an InterCity train headed by a class 103 electric locomotive clearly visible in the background. Both weren't put into service before the early 1970's.
The automobiles driving down the street outside the elderly-pension office (around the 25 minute point) are clearly the type of cars typical of the mid-1970's, even though the scene was set in November or December 1963.
Roschmann was supposed to have a limp from when he escaped by jumping from the train toilet window, yet when he leaves his firm's exhibition and runs to a waiting car there is no hint of a limp (runs like an Olympic sprinter); but it re-appears later when he is confronted by Miller at the castle.
In the opening credits Peter's Mercedes comes to a stop at a light, and he waits for pedestrians to cross. When the camera cuts back to his car, all the cars around him have changed, including a bus that appears behind him.
The scene where Peter is in Karl Braun's flat and they are drinking beer at the table. Karl pours a beer for Peter which is a regular beer colour, he himself has a Dunkle [dark] beer in a tall glass. After the children have come and gone from saying goodnight, Karl's beer has changed to the same as Peter's and in a similar small glass. There is no sign anywhere of the beer in the tall glass.
Silencers on revolvers don't work, as they have a gap between cylinder and barrel from which sound and gases escape, thus silencing the muzzle would not have much effect. The only major exception to this is the pre-WWII Soviet Nagant M1895 revolver (not used here), where the cylinder moves forward before firing, effectively sealing the gap. The silencer for this revolver was quite effective but also conspicuously large.
Peter Miller infiltrates the Odessa organization by claiming to have been a member of the firing squad which executed Admiral Canaris at Flossenburg concentration camp in April 1945. Canaris was hanged on the gallows rather than shot for his role in the attempted coup against Hitler in July 1944. Franz Bayer who interviewed Miller and accepted his story would have known this and therefore deduced he was an imposter and didn't serve at Flossenburg as an SS guard.
On the back of the Volkswagen ambulance that takes Tauber to hospital, it says "Unfallwagen". The correct German term for "ambulance" is "Krankenwagen". "Unfallwagen" is a term used in Germany among car dealers and means a car that had an accident ("Unfall") and is restored.
In the final scene, Old Marx is in Jerusalem, alone in the Hall of Remembrance "saying Kaddish." Kaddish must be said by a minyan of at least 10 men, otherwise it is not considered Kaddish. Therefore, Salomon Tauber's request would also most likely not have been for, essentially, one person: "will some kind friend please say Kaddish for me?"
So, what's with the watch? Peter Miller (Voight) at least twice when talking to the head of the Israeli intel team (Peter Jeffrey) asks about his watch: "I want my watch..." But the significance of that watch is never addressed - was something left on the cutting room floor?