Around 17 minutes into the film, Christopher signs for a folder of top secret material. The two signature lines above his show signature dates of 1984, even though this scene takes place over ten years earlier.
At the border crossing, "Snowman's" Mustang has the license plate "213-IMW" but on the computer terminal in the field marked "plate number" the U.S. border guard enters "NRQ410" (echoed back on the screen as "NNRRQQ441100") which is clearly the wrong plate. NRQ could stand for "NARCOTICS" as sort of an in joke by the producers.
A Russian addresses Daulton as "Comrade Lee." The title "comrade" was reserved for fellow Soviets, especially Communist Party members. No ordinary non-communist foreigner would ever have been called "comrade," but rather "Mr."
(at around 1 min) The scene where Chris walks into work and several close-ups are shown of incoming telex transmissions has some date discrepancies. The very first telex shown right before Chris walks in the door has a date stamp of March 2nd, 1976 while others in the scene say September 9th, 1974. Also the cipher card he pulls out of the binder that day is marked for September 1st, 1974.
In the beginning of Falcon and The Snowman, Dalton (Sean Penn) is talking to his attorney in a conference room. During the conference, Dalton's attorney refers to him as "Sean" during a heated discussion. The attorney says, "Sean" in a stern, attention getting voice.