Continuity mistake: When Roseanne is talking on the phone to Jackie, she continually moves around the kitchen while preparing dinner. The extra-long phone cord goes from being completely wrapped around her waist to just being behind her, then wrapped around her again, without moving in a way that would unwind it.
Plot hole: Before her date, Becky asks Roseanne to help style her hair. After the family teases her, Becky says she'll just do it herself. Shortly after, she comes downstairs with a perfectly executed and complicated French-braid hairstyle that would be all but impossible to have done by herself and in such a short amount of time.
Continuity mistake: Darlene and Becky's second-story bedroom window is on the side of the house and at the house's backside (D.J.'s room is at the front and the windows are also on the side). However, when the girls argue and throw each other's items out the window, everything falls into the front yard, as viewed from the living room. Even if they threw stuff from the house's front, the roof extends too far out below two smaller upper windows. Everything would land on the roof.
Scenes from a Barbecue - S3-E24
Plot hole: All the kids and Arnie are about to play a basketball game. Darlene and Chuck Jr. battle in Rock, Paper, Scissors to see who picks first. They both throw scissors, and then Chuck Jr. says he gets to pick first. They should have done it over, since that would be considered 'a tie', he really didn't win. (00:12:10)
Scenes from a Barbecue - S3-E24
Continuity mistake: Becky went from having long hair throughout this season to having very short hair in the last episode (ep. 23), then back to long hair in this episode (ep. 24).
Suggested correction: I'm not sure what the ruling on these types of mistakes is, but "Dances with Darlene" (ep23 and production code 425) was aired out of order. It was the last episode filmed in the season and meant to be a season finale, but aired prior to "Scenes from a Barbecue" (production code 423). One reason seems to be this is a Mother's Day episode and aired on the Tuesday before Mother's Day, and the next episode was Jay Sanders' last appearance.
The Pied Piper of Lanford - S3-E25
Continuity mistake: In Ziggy's first appearance in the series (S2, EP. 16 "Born to Be Wild"), he says he has two kids. He states "I had to make mine. I checked them at birth, they're boys!" However in his second appearance in the series here, he states they were his girlfriend, Jill's, kids and the kids are back living with their father.