At the five minute mark Colonel Klink takes off his scarf and folds it in a mess, but in the next shot it is perfectly folded, and then in the next shot it is in disorder again.
The bunk with the stairs to the tunnel is shown in the middle of the room in this episode, with the men climbing out of the right side of the bunk from the tunnel. In later episodes, the bunk is next to a wall, and the men can only climb out of the left side of the bunk.
When the truck goes to pick up the POWs from the second camp the sides of the canvas top are rolled up and it is obvious that they are empty. After Schultz leaves the truck Hogan and Carter are shown to be hiding in the rolled-up sides. None of the guards at the front of the building notices them suddenly appearing. Update: The six prisoners were picked up from General Schmidt's headquarters.
When Sergeant Walters is telling Hogan about the unfinished mission, he questions Hogan about completing it, since it is 50 miles away. Later, Klink sets up a truck run to pick up the additional six prisoners from General Schmidt's headquarters. The truck arrives at General Schmidt's headquarters late in the evening (it is dark when they arrive at the headquarters, and the General's fraulein says it is late). However, when they arrive back at Stalag 13 it is near midday (check the shadow the guard in the background is casting - it is very small). This would seem to indicate that, once Schultz arrived at the General's headquarters, it took approximately 12 hours to get the prisoners loaded into the truck and drive the 50 miles back to Stalag 13. The 12 hours is based on the assumption Schultz arrived at the headquarters some time between 10 and 11 PM, and arrived back at camp some time between 10 and 11 AM. At that rate, they could almost have walked the prisoners back to camp. Also, there is no indication that Schultz stayed somewhere overnight - certainly not the General's headquarters, as Klink tells the General that his headquarters blew up the night before.
Just after the introduction, Hogan is talking to Sergeant Walters about the situation with the Sergeant's mission, and his intent to complete it. It's a 50 mile trip to the site, so Hogan goes to Klink to set up transportation. When Hogan walks into Klink's office, the shadow of the microphone is visible on the corner of Klink's desk - the corner nearest to the camera.
In some scenes, production lights are reflecting in Klink's monocle.
Sergeant Walters is escaping. Earlier, he officially became a prisoner at STALAG 13. There is no mention of the escape not breaking the 'no escapes' record of the camp.
General Schmidt is seen playing chess with himself in the barracks. Nothing was said about which barracks he was assigned to after he was 'captured'.
Carter is not married, yet he is seen wearing a wedding ring.
When Hogan goes to Klink to incentivize him to get the six other prisoners, Hogan mentions that the other six went to Kleinfeld. However, when Klink calls to get the other six prisoners, he calls General Schmidt's headquarters. How did he know to call General Schmidt's headquarters? He knew they were captured at Schmidt's headquarters, but there was no indication that the other six prisoners were still there. Since Sergeant Walters already arrived at Stalag 13, the other six prisoners should already have been sent to Kleinfeld, and Klink should have called Kleinfeld.
When Schultz arrives back at camp, there is no indication that a guard was in back with the prisoners. Hogan actually suggests that one fell out due to the bumpy roads. There is no way that a guard would not be in back with the prisoners to prevent them from jumping out.
When Klink is showing Hogan the list of prisoners that just arrived from General Schmidt's headquarters, he does not notice that there are seven names on the list (instead of six), nor does he notice that the seventh name is not in the same handwriting as the other six names (since Hogan wrote it in).