Chapter Two: A Touch of Evil - S1-E2
Continuity mistake: During the pep rally it is raining hard and everyone on the football field is soaking wet, but when Cheryl runs from the field into the locker room followed by Veronica and Betty, they are all completely dry and their hair is perfectly styled.
Chapter Four: The Last Picture Show - S1-E4
Continuity mistake: Archie and Betty are shown as living in houses next to each other, but in shots of their houses, Betty's address number is 111, while Archie's is 2037.
Chapter Four: The Last Picture Show - S1-E4
Continuity mistake: When Ms. Grundy and Archie are watching a movie, her hair switches between shots from behind her ear to in front. (00:14:40)
Chapter Two: A Touch of Evil - S1-E2
Continuity mistake: At the pep rally everyone says it is raining - on stage mayor McCoy is holding a soaked umbrella while around her no-one is wet, and we see all the cheerleaders completely dry at that moment.