Other mistake: Erin at the beginning of the episode records her acting using a camera on a fixed support. She gets interrupted once. She resumes then. The camera angle is different, and then simply changes (as it's made clear by Magnum rewatching later the actual tape) without anyone else operating the camera.
Magnum, P.I. (1980)
1 other mistake in Skin Deep - chronological order
Starring: Tom Selleck, Roger E. Mosley, John Hillerman, Larry Manetti
Don't Eat the Snow in Hawaii - S1-E1
Continuity mistake: When Magnum drops the ring out of the envelope, nothing is near it as it's shaking. In the close up shot, it's next to keys. (00:44:20)
Mac: Time has little to do with infinity and jelly donuts.
Trivia: At the awards ceremony, three men seated at a table together resemble three detectives from 1970s TV shows. Detective Mike Stone (played by Karl Malden) from ABC's Streets of San Francisco; Detective Frank Columbo (played by Peter Falk) from NBC's Columbo; and Detective Theo Kojak (played by Telly Savalas) from CBS's Kojak. (00:07:20)