Factual error: Ray, Sara, and Kendra are Left Behind in 1958. However, 10 weeks later Sara and Kendra are playing the board game "The Game of Life." The modern version, as seen, didn't come out until 1960 (previously it was called The Checkered Game of Life and doesn't resemble the modern version).
Factual error: In 1993, when Jefferson's father James comes to the hospital to see his son after he is born before he deploys to Somalia, he is wearing his rank upside down on his uniform collar, and he has no rank on his headgear. Also, he wore his headgear while he was indoors for the duration of the episode. Headgear is not authorized to be worn while indoors except in certain cases, none of which would have applied while he was in the hospital visiting his son. (00:18:15)
Character mistake: After Ray Palmer says he's an Eagle Scout, he says to Leonard Snart, "be helpful to others, scout's motto." The Boy Scout's motto (including Eagle Scouts) is "Be Prepared." "To help others at all times" is part of the Scout's oath, but that's different than its motto and not something an Eagle Scout would mix up.
Continuity mistake: In the scene aboard the Waverider when the crew discusses their discovery of the Oculus, the first two times you see Sara sitting on the Captain's chair from the back she's leaning forward with her elbows on her knees. When you see her from the front, though, she's sitting with her legs crossed and her right hand on the control panel, and in a following shot you can see her actually change her position and lean forward. (00:23:45)
Factual error: At the beginning of the episode, when Snart stole the female soldier's keycard in 1986, she is wearing the U.S. Army's Combat Infantryman Badge (CIB), a combat award for infantry and Special Forces soldiers. It is not possible for a woman to have a CIB in 1986 because infantry and Special Forces were closed to women at the time.
Plot hole: It's revealed that Chronos is Mick from the future after he was abandoned by Snart. However, in the episode White Knights (episode 4) the earlier version was able to sneak up on Chronos and surprise him with an attack from behind. If that was a future version of Mick then surely he would have remembered the attack coming and could not have been so easily caught off guard.