Factual error: When Roy is electrocuted and falls from the roof, after Karen uses the defibrillator paddles on Roy, she lifts both paddles, looks at the EKG monitor and says "He's converted." How exactly could Karen have known that he's converted? It's impossible for the EKG monitor to show anything at all. Either the defib paddles have to be in contact with Roy's body for the "quick-look" to get a reading, which they weren't, or the ECG electrode discs have to be on Roy's chest connecting him to the EKG monitor, and they weren't. As an aside, just watching Marco having problems attaching the air mask, and quickly glancing up towards the camera frustrated, then giving up is priceless.
Visible crew/equipment: After Charles confronts Choi Sung Ho about the candy, Ho explains that he sold it on the black market to buy real food, and when Ho reenters the mess tent through the side door, we can see that outside there's a director's chair, which actors also use, with something printed on its back.
Visible crew/equipment: Near the end, while John is working alone in the mill Ben shows up, and when Ben asks, "Need some help," a crew member is hiding behind the stack of drawers, toward the right side of the screen. It's not Zeb or Easy or any family member. (00:46:30)
Continuity mistake: In Season One, Episode 10 "The Prankster": Just after Otis makes the ghost sounds from inside the house, it shows the gang standing together outside the house. Otis is with them outside, which is impossible, as he is inside the house pretending to be the ghost.
Factual error: Rhodes views the silent movie and the film breaks, leaving the last frame frozen on the screen. Wouldn't happen. When 16mm film broke in 1970s projectors, any portion that jammed in the mechanism was exposed to intense heat from the projection lamp, and would burn. (00:35:30)
Continuity mistake: Towards the end of the episode, Maude makes Walter breakfast and lists some things she will get done around the house. One is to paint the kitchen chairs. She spray paints the chair with Walter in it - the amount of spray paint on Walter's jacket changes thoughout the scene, especially when Maude is on the phone turning down a job.
Other mistake: In the "Happy Valley" segment, when the witch is just about to enter the cathedral, you can see a car drive past through the windows behind the altar. (Now, this is Monty Python, so we have to be careful... But is isn't clear, or funny, enough to be there on purpose).
Factual error: 14/11/2013: Amy sails to Ireland from a ferryport in Yorkshire. Ferries to Ireland do not sail from any port in Yorkshire. Yorkshire only has coastline on the North Sea, on the east side of Great Britain, not the Irish Sea, on the west. A ferry from Yorkshire would have to sail right round the country to get to Ireland. We know they're still in Yorkshire, as the paramedics who are called have "Yorkshire Ambulance" on their jackets.