Visible crew/equipment: During the motorcycle chase Rambo jumps over the train tracks, if you look close you can easily see the ramp. (00:18:00)
Visible crew/equipment: In the shot of the stolen army truck crashing through the police road block, you can see a camera mounted inside the truck. Look in the small window on the rear wall of the cab. (Apparently both this shot and the shots from inside the cab were done in the same take.) (01:13:10)
Visible crew/equipment: At the beginning of the movie, Sheriff Teasle escorts Rambo to the outskirts of town. As the sheriff drives off, the boom mike is visible in the reflection of the car's right rear passenger window. (00:07:30)
Continuity mistake: When Rambo has Teasle up against the tree with the knife, it is under Teasle's throat, but in the next shot the knife is to Teasle's right without Rambo moving it.
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.