Character mistake: When the zombies break into Buffy's house, she stakes one to check if it's a vampire. But she should know full well that it isn't a vampire as they all broke into her house without being invited.
Touchstone - S2-E14
Character mistake: The team are finding out who could have stolen the weather device from Madrona and find an energy spike at the same time SG2 are on a mission. "But SG2's mission is galaxies away from Madrona" Says Teal'c. At this time the only missions the teams could go on was in our own galaxy and couldn't be galaxies away.
Wax Doll Castle Murder Case: File 2 - S1-E8
Character mistake: Hajime's proposed solution is obviously wrong, but not for the reason they mention; the 'killer' could never clean themselves up completely and effortlessly in such a short time from the soot.