Corrected entry: Dude, the deputy, is on the road at the end of town to take the guns away from those that enter town. This was pointless. Nobody is watching the other end of town. When Nathan and his men came to town, all they had to do to avoid Dude was ride in the desert and they could have entered the town anywhere they wanted.
Corrected entry: In the scene before Dude and Chance follow the man who shot Wheeler into the bar, Chase asks Dude how he knows he is still in the bar. Dude says he can see the door and there is only one door. Then Chase says "I'll take the front door and you go through the back door."
Correction: Dude says he can see both doors from where he is, although the audience can only see one door.
Correction: This is wrong, but it is not clear from the movie. You can find it in the book. The Rio Bravo didn't have "the other end" to come in through. The town was built under a large rock with only one entrance from one side.