Worf's necktie when talking to Eli (before Alexander's warning) and right before he is hit from behind with a chair.
When the scenes are shot in the Engineering area, Data's eyes are supposed to be 'golden' but in several shots of his face, his eyes are blue.
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.
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 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.
In engineering, Lt. Commander La Forge takes apart the Personal Access Display Device (PADD) that contains Dr. Crusher's play and reveals a common 21st century, circuit board layout. The Art or Visual Effects (VFX) department should have designed a fictional-futuristic circuit board, but instead it appears to have two common integrated circuits (PLCC or ROM) chips next to each other. It is doubtful that computer technology would look this way in the 24th century.
Although the program takes place in Deadwood, South Dakota, a map of Arizona can be seen in Worf's office.
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.
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".
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.
Although Data is unable to use contractions in his normal speech, he tells Riker and Geordi "y'all must be mistaken." Data has been shown able to use contractions when quoting other people, or delivering dialogue in a play, but this scene takes place after they have left the holodeck. This is explained in the story by some of the computer's recreational database accidentally corrupting Data's speech code.