The Hounds of Baskerville - S2-E2
Deliberate mistake: The army major wears a full beard. British Army personnel may not wear beards. (The beard is a nod to the original canon character on which he's based, John Barrymore, who is described in the book multiple times as being a "black-bearded man").
Deliberate mistake: The police car Steve & Danny are driving on the bridge as they approach the freighter has 467 on the roof, which then becomes flipped & backwards a few shots later as they take a sharp right, only to become 467 again (as Danny has conversation with Rachel). (00:38:10 - 00:39:05)
Deliberate mistake: Season 2, episode 10: After Matt is supposed to be dead underwater, you can see air bubbles coming out from his nose in a close-up, and in a far away shot his head is above the water so the actor can breathe.
Deliberate mistake: When Fluttershy is telling off the cockatrice, her back legs and her wings turn to stone. But when she gives it the stare and the camera is right in her face her wings are outstretched.