There's No Place Like Home - S28-E16
Character mistake: The old photo of Sylvia and her friend shows them in RAF uniform. Sam, who is a serving British Army officer and could be expected to recognise the very obvious differences between the uniforms, keeps referring to Sylvia being in the Army and Sylvia does not disagree with her.
The Singer - S7-E5
Character mistake: Near the end, Matlock says that he can prove who killed KC. The burden of proof lies with the prosecution; as a defense attorney, Matlock doesn't have to prove anything.
Yomigaere! Eiyuu Densetsu - S1-E1
Character mistake: Not to dispute physics in an anime about people drawing arcane cosmic powers from constellations, but when Marin explains to Seiya what happens when you shatter a rock into smaller pebbles, she says that you "destroy its atoms." That's not how physics works and luckily for her, Seiya and everyone else in Greece at the time, she did not create a nuclear fission in the palm of her hand just to prove her point.