Factual error: When the boys are sent back to the Cretaceous era, they come across a leptictidium, a small, bipedal mammal they call "Leppy." Leptictidium were not around in the cretaceous, they didn't appear until around ten million years after the dinosaurs went extinct, in the early Paleogene. They also lived in Europe, not North America.
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.