The silver Jaguar in front of Spinoza & Sons is up on a jack in the initial shot - when it cuts to the reverse angle it's not.
During the car chase in Los Angeles sequence, Jock vomits while shooting through the window and the windshield of Strago's SUV is splattered with sick. A second later, when the SUV turns right and escapes, the windshield is spotless clean.
When Hermann Wilhelm Göring is writing his Swiss bank account number on the back of the painting, his armband would be on his left arm, not his right.
When told by Mortdecai that "some members of the fairer sex" find his mustache quite appealing, his wife's response is "Whom, exactly?" This is poor English and unlikely in the speech of a well-educated Englishwoman. 'Whom' is only used to replace 'to who'.
As in: "To who, exactly, would his mustache be appealing?"
As in: "To who, exactly, would his mustache be appealing?"