The way the scenes are edited leave one wondering just how far away the local village is. We see Charles and Mr. Kim leaving the 4077 just as they are starting to set up for the exchange. Charles comments that they haven't much time. He concludes his deal, and heads back. We then see Klinger settling in for his exam--which he must complete in three hours. Charles is stopped by the MPs roughly one hour away from the 4077th on foot. We see Klinger throwing in the towel. He may have quit before the three hours were up--although Potter was shown checking his watch, which implies that time was running out, but it still had to be a fair amount of time. By the time Charles comes running to the barricade, Klinger has had time to get freshened up and into a fresh (Naval) uniform. The village just seems to be too far away. If it was so far, it doesn't seem likely that the 4077th personnel would be allowed to go there, for fear that the war would intrude and they'd need to get back fast.