Shawn tells Gus that Sophie likes Red Robin, and then asks what they serve there. However in the next season when Shawns uncle Jack comes to visit they are scheduled to meet at Red Robin which Jack used to take Shawn to when he was younger.
When Gus and Shawn pull up next to the van at the loading dock, the van's parking lights are on. In an overhead shot the lights are off, and when the van starts the lights are on again.
Shawn mentions that the mummy was in Plano, Texas, but Plano does not have a Natural History museum. There is only the Perot Museum of Nature and Science in downtown Dallas, Texas, which is about 30min south of Plano. Plano only has a Railway museum and a Heritage Farmstead museum.
While looking at the gun case in the museum, Gus tells Shawn about the "bulletproof Lexan Glass." Lexan is not glass, but a type of plastic. It is not bulletproof, but rather bullet resistant, depending on the caliber of the bullet and the thickness of the Lexan.
In the close-up of the newspaper article on the Chief's replacement, the same text from the second column is repeated in the third.
While explaining how human eyes work, Shawn states that the cones are what allow us to see at night. This is incorrect - the cones are what allow us to see in color. The rods are responsible for night vision.