When Claudia is pushing the wheelchair through the mud to the Grand Central for Chesterton, she turns around some crates in front of the hotel, and approaches the ramp to the boardwalk. In the next shot, she is once again turning around the crates and approaching the ramp.
As Jack Langrishe lounges in Al Swearengen's office his shoes reveal modern rubber soles with patterned tread instead of leather soles as would have been found at the time.
In a conversation between Cy Toliver and George Hurst he mentions the term gunsel. This term was used in hobo slang around 1915 to refer to a young male companion of an older tramp. It wasn't until the 1929 novel "The Maltese Falcon" by Dashiell Hammett when the term came to be used to refer to man who was good with a gun. So it's unlikely that it would have been used in Deadwood in the 1870's.
When Bellegarde is in the hotel room helping Chesterton, a modern day, round electric light used to illuminate the characters, is reflected in Chesterton's glasses.