To Russia with Love (1) - S3-E24
Character mistake: While talking with Falcon, Harm mentions the "green book" Falcon stole that listed all of the American POWs transferred to Russia after the Vietnam War. But when Harm originally found the book in "Ghost Ship", its cover was yellow.
Character mistake: Mrs. Reynolds, the housekeeper at Pemberley, refers to Mr. Darcy's late mother as Mrs. Darcy while showing Elizabeth and her aunt and uncle the house. This is a grave mistake on the part of the filmmakers as she should have been referred to as Lady Anne, the way her sister is known as Lady Catherine. Their father was an Earl, making them Ladies by birth, not by marriage. Hence, they must be called Lady followed by their first name.
Character mistake: Captain Janeway states the temporal differential ratio is .4744 seconds per minute (meaning for every minute on the surface, only .4744 seconds pass on Voyager). Tuvok calculates that 30 minutes on Voyager would be 2 days 11 hours and 47 seconds. However, at that ratio, 30 minutes would be 2 days 15 hours 14 minutes and 15.9 seconds. Later Tom (who was on the surface) says the last two months for them was only 2 days for B'Elanna (who was on Voyager). But with the temporal differential, 2 months on the surface would be less than 12 hours on Voyager. 2 days on Voyager would be almost 253 days (almost 8.5 months) on the surface.
Armageddon Now: Part 1 - S4-E13
Character mistake: Callisto's sword is missing. When she appears in the Xena Season Three finale "Sacrifice", her sword has reappeared. It is never explained why Callisto doesn't have her sword during her three appearances on Hercules the Legendary Journeys.