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).
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.
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 flashback to 1920, Kendra flips the calendar to October with a snowy mountain side picture. Later when she's talking to Carter about leaving, the calendar is now on September with a trail through the grass picture. It goes back to October when their son comes in.
Factual error: The quiz on the cereal box asks "who is the most prolific serial killer in the United States", to which Ava replies "Ted Bundy. Although in my opinion, John Wayne Gacy had way more victims than he confessed to." The box also lists Bundy and Gacy (plus the anachronism). 2 things, Gacy was in fact convicted of more murders than Bundy, making him more prolific. But, Samuel Little is the most prolific serial killer in the US and Gary Ridgway is the second. Ted Bundy would rank 6th on most list.
Factual error: When Ray is on the moon, he's getting the spear from the flag that was planted in the Sea of Tranquility, from the Apollo 11 mission. When we see the flag, it's still standing up. However, Buzz Aldrin saw, and reported, that the flag fell over from the rocket's exhaust as they left the moon, and no one from Apollo 12 put it back 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)