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.
Character mistake: In the episode where Henry has overdue library books, they are overdue by 5 years and 23 days. Both Henry and Monroe say in the episode that the fine is around $1000 (based on 10 cents per day due 5 years 23 days)... But in reality, using that calculation, the total would come to only $185, not $1000.
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."