I have watched it since it came on, fairly entertaining. The "uniforms" are a little off, but I do remember when I was living in Central Montana and NW Wyoming, there were Sheriff's and their Deputies who dressed down from the usual uniforms. We need to remember that the show is geared for the American people who probably believe that image is what Law Enforcement is in the West. If they really showed what being a LEO is out there it would just be Longmire leaving the house each morning and taking several boring rides around the county maybe stopping to talk to some ranchers.
I think the best representation or an "old school" modern day sheriff was the character of Sheriff Ed Tom Bell played by Tommy Lee Jones in No Country For Old Men. Every day he just tooled around minding his own business until things exploded due to a botched drug deal. One great moment was when Bell and his Deputy we looking over the drug deal scene with all of the dead bodies and the Deputy said,"Sheriff, this sure is a mess" Bell looked up and said,"if it isn't it will do until the real mess gets here(meaning the Feds).