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)