Visible crew/equipment: The arm of the actual carriage driver is is visible poking through the back of the carriage, slapping the horse and signaling it when to stop/proceed with a second set of reins, showing the actor in the carriage was not controlling the horse at all.
Factual error: At the mint, Arte hides in a broom closet. He carries nothing in (nor did he hide anything in there beforehand), yet he emerges later in an "old man" disguise, wearing a wig, hat, mustache, false nose, glasses and janitor costume. Magic closet?
Continuity mistake: "Night of the Bubbling Death": When Grigsby first approaches the stolen U.S. Constitution, it's under glass (we can see the light reflections). But seconds later he lifts the paper without removing the glass, which has disappeared. It's back later, when West must cut it to retrieve the document.