Factual error: In the classroom where Jack argues with Roger next to the chalkboard we can see a poster of the periodic table of the elements. We can see some elements that wouldn't be there in 1977 since they weren't discovered until 1999.
Factual error: Anytime a character fires a missile at an airborne target, it's invariably from an M136 antitank launcher. The M136 is designed to hit relatively slow moving ground vehicles and is useless against fast moving airborne targets. (This is because used M136 tubes can't be reloaded and are very cheap to use as props).
Factual error: When the large Dutch guy tells his story about his life in Holland, there are a several windmills. However, the blades are placed on the wrong side, that way it's not possible for a windmill to turn clockwise, which it does. If the blades were placed correctly, they would still turn to the wrong side, because wooden windmills in The Netherlands are always turning counter-clockwise.
Episode #1.1 - S1-E1
Factual error: There is a view of the night sky in southern Africa. However, both the Big and Little Dippers (along with Polaris) are visible. In general, these constellations are not visible in the southern hemisphere, and where they are (North of 1° South latitude) they are very close to the horizon. The Big Dipper (Ursa Major) is to the left of the screen and Polaris (part of the Little Dipper = Ursa Minor) in near the top-center. This occurs shortly after the lion cub scene. (00:44:00)
Factual error: In s01e08, "Q and A", when Yelena is playing chess, we see her use the touchscreen which represents the chessboard. However, the bottom left corner is a white square when it should be a dark square. The board is orientated incorrectly, even though the board on the floor isn't.