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)