Nurses in the 1950's and women in general would have on stockings. Nurses always wore white too. The bare leg look is a 2000's thing not a '50's thing.
When Savage is injecting Jefferson with the Meteorite fluid, you can see the fluid being pushed out of the syringe behind Jefferson's lower neck.
When they first arrive in the town, the picture they show for the town is not in Oregon, the hotel Gadsden is in Douglas Az.
Dr. Stein mentions that he did his Doctoral work on "serial murder". In 1958, serial murder was not yet recognized as a criminal pattern. The term "serial killer" was coined in the 1970's by FBI Special Agent Robert Ressler.
The spoken word "slash" is only a recent usage, the doctor should have seemed at least slightly confused by its use in "nurse slash assistant."
Ninjas are mentioned. The first major appearance of ninjas in Western pop culture was a secret commando force used by Japanese intelligence in the 1967 James Bond film You Only Live Twice (1967), according to Wikipedia.
When the two nurses are talking, the one from the future says "This town sucks." and the one from the present says "Wow, you do not hold back.", meaning she understood what "sucks" meant. The slang term "sucks" was not used in America until the 1970's. Similarly, the term "freaked out" is incorrectly used later by the same characters. It came into popular use about 10 years later in the 1960's, usually a reference to drug use.
When the sheriff confronts the "orderlies" in the hallway, a gun cocking sound is heard since he was holding his revolver. However wen the revolver is seen again, it has not been cocked. The gun cocking sound when a gun is seen is a very common TV firearm error, and often involves hammerless guns that cannot be cocked.
Jefferson refers to the sheriff as Boss Hogg, a reference to a character in The Dukes of Hazzard (1979). The error was that Boss Hogg was in effect the Mayor, not the sheriff, who was Roscoe P. Coltrane.