When Danvers is standing in front of the entertainment center in Tsalal Station, the DVD copy of The Thing (1982) changes position from one shelf to another.
The opening coordinates of the Tsalal Arctic Research Station are 68° 65 N, 165° 35 W. This latitude reading is incorrect ("65"), as minute (and second) and second readings cannot go beyond 59.
Season 4 of True detective starts with an Arctic sunset on December 17th. Polar night is centered around the Winter Solstice which is about December 21. if the sunset occurred on December 17th, the next sunrise should occur on about December 25, but darkness is lasting at least through New Year's Day. Also, at approximately 68º N (Tsalal Station's latitude from its sign) polar night should last from December 9 through January 31st.
They wouldn't be police they would definitely be Alaska State Troopers. A town that size and that remote wouldn't have their own police force.
They would most likely be covered by the Fairbanks dispatch that covers the largest area of Alaska. Which includes the interior and the Aleutians.
It's routine for small towns in Alaska to not have any police presence. And common for Alaska State troopers of that dispatch to cover hundred of miles by themselves without any kind of immediate back up.
The thermostat in Martin's home was not available in the mid-1990s.