Revealing mistake: When Rambo throws a rock at the police helicopter and knocks Galt out, you can clearly tell it's a stuntman. Galt is in his 40s and overweight. The guy that was falling looked like he was 25 and was noticeably thinner.
Revealing mistake: In the scene where Rambo is driving the truck and pushes the cop car into path of the broken down car, the explosion starts the second the cars make contact. In the next shot during the fireball, the two cables that held the static vehicle in place are visible.
Revealing mistake: Towards the end of the film where Rambo shoots up the computers in a building and the spent rounds are falling to the ground. It is clear to see that these are blank rounds. Where the bullet would sit in the case normally you can see the case is extended, This is where on a blank it is just crimped closed due to the lack of a bullet.
Answer: At the start of the film when Rambo is causing all these problems, the Sheriff has no idea who John Rambo is (Vietnam War hero), so he thinks Rambo is just another America-disrespecting drifter (the American flag on Rambo's jacket). Also, Teasle is a law and order guy who does not want his town disturbed by outsiders. After the fireworks and Teasle finds out who Rambo is and also meets Colonel Troutman, Teasle's mission becomes personal: rage at the death of his best friend, humiliation in front of his deputies, the incompetence of the state National Guard to subdue Rambo, and also a generational factor: Teasle probably served in Korea or WW2, when America was top dog in the world, so he will not allow some hippie ex-soldier from a "lost" war best him.
Scott215
That's it. When they got the news that Rambo not only was a real war veteran, an ex-Green Beret, he was a war hero with a Medal of Honor; if Teasle's ego was Pearl Harbor, getting that info was December 7, 1941.