When T'Mir and Jack talk outside and T'Mir talks and shown from the front with Jack shown from the back, the sun is shining. When Jack speaks and the camera shows him from the front and T'Mir from the back there is no sunshine. Indicating the scenes were shot at different times and likely used stand-ins.
Several scenes from the dinner table show a fuller bottle of wine compared to the scene right before them.
If the story takes place immediately after the Sputnik launch, the time frame is from 4 October 1957 to January or February 1958. They claim they were watching Sputnik for 3 weeks before they crashed, making the crash date roughly October 25th. They then spent 2 weeks in the woods before coming to town, that would make it November the 8th when they came to town. Yet the weather seems to be summer and fall throughout, which it would not be in southwest Pennsylvania.
They had been observing Sputnik, which was Launched October 1, 1957, almost three weeks before they crashed which would have been close to the end of October. "I Love Lucy" broadcast its last episode May 6, 1957, so it could not have been on TV for them to watch. It would not have been in summer reruns because TV did not broadcast reruns in the summer in those days. Even it had, the new TV season would have started in September more than a month before they crashed.
At one point, T'Mir tells Mistral that the trapped miners are 30 meters ahead. 30 meters is almost 100 ft, yet he takes only three or four steps to reach them about 10 feet (3 meters) in front of him.
When they first walk into the bar, actors' tape marks are visible behind the bar on the floor when they meet the bartender.
When T'Mir and Mestral steal the clothing off the line, they are next seen walking in Carbon Creek with T'Mir now wearing women's pumps. Where did she acquire them.
1990s-design banknotes (most notably a $50 note) are seen in the bar's tip jar.
In the original broadcast and DVD version, the the period-appropriate song "Crazy Arms" by Ray Price is being played when the Vulcans enter the bar. In 2011 when Carbon Creek was remastered for Blu-ray and international distribution CBS replaced it with the 2009 song "Gently Falls" by Dave Colvin, possibly due to copyright restrictions. This change creates a double anachronism of sorts. The song is not correct for the show's 1957 setting, nor did it even exist at the time of the original 2002 broadcast.
The paper grocery bags have handles that didn't become available until the late 1990s.
At approx. 21:11 a modern day "Chains Required" CA DOT sign can be seen alongside and partially covering a modern era "35 mph speed limit" sign.
Several times during the episode a pickup truck can be seen with raised white letter tires. Those tires are a minimum 10 years too new for late 1957.
Mestral may have mastered geometry, and have great hand-eye coordination, but he would not know the rules of pool well enough to play flawlessly and fake being familiar with the game--not against a pool sharp like Billy.
Carbon Creek being a small town one would think the owners of the stolen clothes are patrons of the bar. It is possible at some point someone may have noticed they had their stolen garments.
When they are preparing to use the particle weapon, T'Mir tells Mestral to set the "dispersal radius to 7 degrees". A radius is a measure of distance. She should have told him to set the dispersal angle.
At 24:33 the Vulcan officer lies to his female captain. This goes against the idea that Vulcans could not lie.