Factual error: The helmet is a Cooper/Bauer HH3000 that wasn't made until 1989 or 1990. (00:26:30)
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: A scene shows a Wyoming ANG C-130H with 6-bladed props and a modern striped tail flash. The shown aircraft, tail 37314, was made in 1993 and assigned to Wyoming ANG around 2007. In the 80's the Wyoming ANG had much older C-130B aircraft. The stripe style tail flash didn't come around until the mid-1990s. In the 80's Wyoming C-130's would have had a large black "WY" on their tail. The 6-bladed props didn't appear until after 1999 (first on C-130 J models). (00:03:48)
Other mistake: When Phillip is in the pastor's office, the book Partners in Power can be seen on the bookshelf behind the pastor. That book was published in 1996, and pertains to the Presidency of Bill Clinton.
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)
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.
Factual error: The mural on the diner wall shows the 21st century Afghanistan campaign medal and operation Iraqi Freedom campaign medal.
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.
Continuity mistake: Elizabeth sustained a fairly severe wound to her back (left side, if I remember correctly) a little above her waistline, but no scar appears in subsequent episodes.
Continuity mistake: In an earlier episode, FBI agent Stan is shown parking on the left of the drive and going into the house on the left. In episode 2.8, Elizabeth is shown coming out of her house to see the New Car, but it's the same house on the left that was shown to be Stan's house earlier. Same house used for both families.
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.
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)