Worf's necktie when talking to Eli (before Alexander's warning) and right before he is hit from behind with a chair.
Worf is wearing boots with tapered "dogging" heels, These are designed to dig into the ground when "bull dogging." A town sheriff (who would not be doing such things) would be wearing standard boot heels because they are more steady and last longer.
When Durango is practicing her quick draw in the Sheriff's office, she fails to cock the weapon as she draws. Since most revolvers of the period were single-action, the weapon would not fire as she pulls the trigger.
When Frank and Eli Hollander (at this point both played by Data) are talking at the prison on the holodeck, the side of Data's left arm seems to be cut off as he turns to walk away. This is due to the split-screen technique used to show both Datas in the same frame.
When Frank Hollander walks away from the prison cell toward the camera, we see Eli Hollander behind him in the cell. Both characters are played by Brent Spiner, but in this shot we see an obvious stand-in for Eli.
In the establishing shot of the frontier town, the building at the left is clearly no more than a dozen feet deep.
Although the program takes place in Deadwood, South Dakota, a map of Arizona can be seen in Worf's office.
Crusher, in trying to convince Picard to act in her play, tells him that the rehearsal is at 1:30. While she could mean 1:30 am, it is well established that the Enterprise department heads, barring a crisis or emergency, operate on a schedule closer to the real-world "9 to 5". If so, Crusher's rehearsal would be at 1:30 pm, which she would refer to as "1330 hours".
Worf has been shot in the arm. When Durango wraps her bandanna around the wound, she wraps and ties it loosely, rather than wrapping it tighter to help stop the bleeding.
On Eli Hollander's wanted poster, the town name of Bozeman, Montana is misspelled as "Boseman" twice.
At the beginning Captain Picard states they were in orbit around the planet Deinonychus VII but their scheduled rendezvous with the supply ship "Biko" had not occurred; Picard pronounced it as 'beeko'. Steve Biko was a South African activist whose name was properly pronounced "bi-ko". Sadly, the proper pronunciation was not given to Patrick Stewart, since it was likely chosen in honor of Biko's death in 1977.