Factual error: Throughout the first season, set in the early 80s, the two Russian agents are shown carrying and using 3rd version Beretta P92F semi auto pistols. The P92F didn't come out until 1988.
Factual error: In nearly every episode shot outside in city neighborhoods just out of the camera's focus you can see so many cars from the late 2000s.
Factual error: The helmet is a Cooper/Bauer HH3000 that wasn't made until 1989 or 1990. (00:26:30)
Factual error: When they are playing hockey in the driveway, the FBI agent says he lived in the city in St. Louis. He then says they had street names like 1st street, 2nd street, Washington, Lincoln. First and Second street exist, but they are both in industrial areas and no-one ever talks about them. More to the point, there is no Lincoln Street in St. Louis at all. (00:27:00 - 00:28:00)
Other mistake: Elizabeth states her father died in Stalingrad when she was 2, which was 1942-1943, and she claims she came to America at 22 when it was 1965 and she would have been 24-25.
In Control - S1-E4
Other mistake: Reagan was shot in March, but Elizabeth is digging her crate from the ground with autumn leaves around her.
Visible crew/equipment: When Phillip is being bundled into the back of a van there are 4 men and Phillip in shot with no-one else on the street. As the van door closes you can see a crew member through the gap in the door. (00:02:56)
Factual error: A German bio-metric passport is shown that was only issued after 2005. (00:14:40)
Factual error: When Elizabeth confronts Sanford Prince in the restroom, there are modern, automatic flush sensor urinals visible. The first automatic flush urinal wasn't invented until 1988. (00:06:46)