It is an entertain show certainly, especially the one where they responded to a moose that was stuck in a greenhouse.
However, I remember an episode once where a guy was arrested for something (DWI or drugs seems the norm) and he also had a small folding liner lock knife on him. The trooper goes "switchblade, can't have that in Alaska"...WRONG...the knife clearly was not a "switchblade" of any kind, it has thumbstuds and looked like a Gerber paraframe in the quick view I saw. The guy was getting locked up for plenty of other things anyway, it just annoys me though to see police get something completely wrong like that.
Reminds me of an episode of Cops in which an officer in Florida held up a knife they took off a guy to his open palm and said it was illegal because it was longer than 4 fingers width. PRECISELY NOWHERE IS THERE A LAW THAT DETERMINES A KNIFE'S LEGALITY BASED ON A NONSTANDARD MEASURE LIKE A PERSON'S HAND WIDTH.
A sad piece of trivia about the AST show, since it has been on (since around 2010 I believe), 3 troopers who have appeared on the show have died in the line of duty.