Other mistake: With power out Magnum somehow lights the gas stove with the knob, which is electric. Should have used a match. (00:26:40)
Galactica Discovers Earth: Part 1 - S1-E1
Revealing mistake: When Troy and Dillon land on Earth, they take their bikes onto the freeway. They're followed by a large group of curious bikers. When two of the bikers move alongside Troy and Dillon and start talking to them, it's obvious that all four bikes are now mounted on a trailer, instead of riding on the road. Easiest way to tell is that their heads are higher up than the other bikers and the front wheel isn't turning.
Deliberate mistake: In the scene where the ministers are all crammed into the train carriage if you look over Jim's shoulder there is a sign ("Notice" "In case of Fire" etc), while the headers are in English the actually paragraphs are written in gibberish.
Break Out the Pampers: Part 2 - S3-E2
Character mistake: Near the end of the episode, when Ms. Rafkin stops by to see the Rush family, Sara greets her by name. Ms. Rafkin (who thinks her looks have changed due to a facelift) asks Sara how she knew it was her. Henry told her by her voice which she accepted as the answer. This wouldn't be a possibility since Sara said hello before Ms. Rafkin spoke.
Episode #1.1 - S1-E1
Character mistake: In the opening minutes of the first episode, as the Erasmus is struggling through a storm, Blackthorne is told that the boatswain is dead. He checks the corpse and then says, "Get the body aloft," which would entail carrying the deceased up the mast. The correct order would be "Get the body topside."