Deliberate mistake: Robert Brown wears a gold turtleneck sweater with his leather outfit throughout the series. Though it's more than 100 years beyond the show's 19th Century setting, he and the producers decided that he looked good in it, so allowed the anachronism to stand.
A Sour Note - S2-E2
Factual error: Gino commits a murder using a six-shooter with a silencer attached, and his shot doesn't make any noise. But it should have. Though it's a long-standing Hollywood cliché, a revolver with a silencer wouldn't be silent at all. Unlike automatic weapons, revolvers are open-chambered, which allows sound to escape. They can't be muffled with a silencer. (00:34:00)
The Incomparable Connie Walker - S1-E18
Continuity mistake: "The Incomparable Connie Walker": When Dillon visits Mayor Walker's house, Walker's red carnation is on his left lapel. But one shot of him is, for some reason, reversed, causing the carnation to switch itself to his right lapel for a moment.