When Stan opens the trunk, the Oldsmobile nameplate is still askew, revealing the keyhole, yet when Stan closes the trunk, the nameplate is straight and the keyhole is covered. Stan didn't move the nameplate.
During the kitchen confrontation with Elizabeth, the position of Philip's hand on the knife blade changes between shots.
The high beams of the headlights of the car go on and off when they are swapping the license plates.
The pilot for 'The Americans' starts off with historically inaccurate information. Two guys are talking about some tough guy who allegedly took out 4 Olympic Japanese judo players in a bar fight. And the other guy says "Which year? Because The Japanese didn't medal in Judo from 1964 to 1972.".... In fact the Japanese won 3 gold medals in 1964, skipped the Mexico City Olympics in 1968, then won 3 more gold medals in 1972, and 1 bronze.
Just after Philip and Elizabeth change the license plates on their car from DC to VA tags and begin to head out of DC to their Northern VA home with the body in the trunk of their car, they discuss which would be a faster way to get to the beltway (I-495)--the George Washington Parkway or I-66. I-66 did not open until August 1982, well after the supposed 1981 setting.
In the flashback scene when Elisabeth meets Phillip for the first time at KGB headquarters, they drink tea from glasses on which the two-headed eagle is portrayed, coat of arms of the modern Russian Federation state.
IBM Personal Computers are seen in the FBI offices. The series in set in early 1981 and the IBM PC was not introduced until August 1981.
At the beginning, the song "Harden My Heart" is heard on the soundtrack. This episode takes place before President Reagan's attempted assassination. The song was not released to the public until about nine months later.
In the mall scene, "Harden My Heart" is clearly playing over the store's sound system (not just in the show's soundtrack). In the early '80s, mall department stores did not play current-year pop songs; they would have been playing instrumental "musak" versions of much older tunes.
The hockey equipment being used is a mish-mash of 90's (helmets) and early 2000's (skates, gloves) really only the jerseys are close to authentic for the early 80s.
(at around 1h 0 mins) As Agent Bartholomew opens the door to the meeting, a crew member (red short-sleeved shirt) is briefly visible in the room.