Audio problem: When Rambo rides the motorcycle down the sidewalk he's shouting at the pedestrians to look out. The movements of his mouth don't match what you hear him say. Originally Rambo was swearing but this was changed.
Audio problem: When the Colonel arrives at the tent we hear the Sheriff say "We're a little busy this morning Colonel, what can I do for you?", but the movement on his lips does not match what we hear.
Audio problem: In the scene after Rambo holds the knife to the Sheriff's neck, we see the sheriff in the tent having his neck looked at by the doctor. The other guy, Dave, says that Rambo is now his problem. The Sheriff then replies, but the movements of his mouth do not match what he says.
Audio problem: In the helicopter scene when deputy Gault is telling the pilot "If you don't fly this thing right...." it would be impossible to hear him over the sound of the aircraft without yelling, yet Gault speaks in a normal voice.
Audio problem: After Rambo turns onto the dirt and rock road, it looks like he is shifting gears, but the sound of the engine doesn't match.
Audio problem: In the shot early on, where Teasel jumps his car and breaks a fence post, his car horn beeps when the car lands on the ground. A few shots later, when his car falls down, then flips over on the embankment, the car horn gets stuck. It's a totally different car horn sound this time.
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.