Factual error: Col. Trautman should be wearing his rank insignia on the flash (small patch) on his beret. All officers wear their rank on their flash, enlisted men wear the unit crest. (This error was corrected in Rambo II and III.)
Factual error: The military cannot be used to help execute civilian law except during emergencies. Rambo could, I guess, be considered an emergency however, once the national guard was called out, they would have had jurisdiction over the Podunk police department. When Brian Denehy told them to wait for them, and then subsequently to clean up their mess, he would not have been in charge at that point.
Factual error: In the scene in the police station, where Rambo was about to get shaved, he had a flashback of the vietcong guy slicing his chest up. The vietcong guy was noticeably speaking Cantonese instead of Vietnamese.
Factual error: The state police cars have light bars that show blue on the left and red on the right. In real life, the light bars would be red on the left and blue on the right.
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.