The League of Villains - S3-E16
Factual error: As the villains are approaching to Earth, South America is shown just under Asia, connected to the Arabian Peninsula and the southern tip of India. The two continents are nowhere near enough to each other to be seen at the same time from space, much less connected. They are on opposite sides of the Pacific ocean, over 10,000 miles (16,000 km) apart. (00:06:45)
Factual error: When Johnny and Bruce are riding in the truck, listening to the 'shock jock', Bruce turns off the radio by turning the volume control on the left side of the radio. Johnny says he wants to hear it and turns the radio back on by turning the knob on the right, which is the tuning dial.
Factual error: Jayne doesn't need the suit to fire his gun, because ammunition contains an oxidizer that would allow it to be fired even without oxygen present.
Suggested correction: From a different perspective it's not a factual error. Because Jane shot multiple bullets. It means the gun still can be shot after the space suit case got pierced from the first bullet. So it's a possibility that the characters thought wrong (even though it's a bit silly for space travellers to not know this fact but doesn't mean it won't happen).
Factual error: In the opening sequences of the show, B-17s are over the Ruhr in August 1944, and yet they're being attacked by nothing but yellow-nosed BF-109E's. The yellow nose was discontinued at about the end of the Battle of Britain, and the "E" model was discontinued even before that.