Continuity mistake: Beltik rolls up his right-hand sleeve. Says, "Hell no" to the offer of a draw. Other side tips King. When they shake hands, Beltik's sleeve is back down, then back up.
Character mistake: During Beth's final match against Borgov, the position she stops to think about features her Queen on D3 and Bishop on E3; however, the staff member operating the spectator display board has these pieces on C3 and D3 respectively, and since this places her dark-squared Bishop on a light square, it's particularly confusing as to how he would have made such an error. (00:55:00)
Character mistake: When it shows young Beth with her mother in the car, she has blue eyes. Her character is meant to have brown eyes.
Adjournment - S1-E6
Factual error: The song in the car when they were heading to New York was released in 1979, but this scene is set in 1967. (00:01:04)
Suggested correction: The song playing is "Stop Your Sobbing" by The Kinks, which was released in 1964. What you're talking about is The Pretender's cover version from 1979, but that's not the version heard.