When Sam, Dean, Jody, and Donna are getting into the Impala to go to the farm, Donna sits behind Sam and Jody sits behind Dean but when they get to the farm Donna is behind Dean and Jody is behind Sam.
When Sam, Dean and Sheriff Donna are tied to posts in the barn, Sheriff Donna uses her broken eye glasses and Dean uses a protruding nail to cut through their ropes and get free. Modern eye glasses are made of plastic and unable to cut through a thick rope. And it's highly unlike in the time given Dean could cut through a rope with a nail.
Even though she is wearing a name tag that says "Sheriff" on it, "Sheriff" Hanscum would not be wearing a blue "Stillwater Police" uniform. The uniform that she should be wearing is brown Washington County Sheriff's Office (WCSO), which is headquartered in Stillwater, Minnesota. All Sheriffs wear brown uniforms, not blue.
Jody tells Donna that she did not want to come to the sheriff's retreat, she only came because the mayor of her town insisted she go. Mayors are only in charge of city police, typically a city's chief of police reports directly to the mayor. However Jody is a county sheriff, not a city police officer, her jurisdiction is an entire county, not just one city. A county sheriff is an elected position so Jody only answers to the county voters and the governor of the state.
When Donna gives the address she found to Sam, he searches the address on his phone. But as we see, he begins typing into a Notepad window on his smartphone, but then hits a button and it gives him search results as if he used a search engine.
When searching looking up an address in his phone, Sam enters it into an "Untitled Note" on his phone rather than a search or mapping app, which results in a map location nonetheless.
Sheriff Len Cuse's uniform reads "Hibbing County, Minnesota". There is no Hibbing County in Minnesota. The City of Hibbing is in St. Louis County.
When Jody examines the personal effects of the victim she fails to put on gloves before touching the clothes. Even if they had already been processed for evidence it is still standard procedure to wear gloves when handling evidence, there could always be a possibility of the evidence needing to be reexamined. Plus if it is a criminal case that winds up in court the defense typically has the evidence analyzed again by a third party, which requires the evidence remain uncontaminated.