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: The American flag in the gymnasium of Beth's first competition is hung incorrectly. The correct way to hang the flag, if hanging it vertically, is to display the stars in field of blue in upper left corner, not as displayed in the film. (00:31:00)
Continuity mistake: The lady asks her for three packs of Chesterfields, at the store, the shopkeeper gives her just one pack, and she can be seen holding and walking with just one pack. When she returns to the house, she puts three packs of Chesterfields on the kitchen counter. (00:24:37 - 00:26:11)
Factual error: Just before Annette Packer and Beth begin, the host pumps some water out of a cooler. I don't recall seeing that kind of dispenser - usually for coffee or hot water - until many years later.
Continuity mistake: The first time Beth plays Beltik she starts the game as black but finishes the game as white.
Suggested correction: Maybe you're thinking of a different scene. When she's waiting for Beltik, she's playing white. You even see she's moved her pawn and it's white. When Beltik shows, he moves his black pawn.
