The airplane they are working on in the tunnel is not the same plane that flies off at the end. The canopy on the plane in the tunnel is much larger and of a different shape.
Also, a plane that small would not have the range to reach Germany from England.
The plane is seen taxing across the compound and then, after a reaction shot of Klink, it's seen flying above the same part of the compound.
Recurrent character Colonel Crittendon: There is no rank of Colonel in the RAF. He is meant to be a Group Captain. Possibly the show's makers believed a US audience would not know what a Group Captain was. His rank insignia, four stripes, have the upper stripes faded. (Apparently he was referred to as Colonel on the show to clearly display to the audience that he and Hogan bore equivalent ranks).
When Hogan tells the Baroness that the prisoners are all Air Force men, he is only partly right. Newkirk is a member of the Royal Air Force but the US Air Force did not exist until 1947. In World War 2, it was part of the US Army.
Sgt. Carter, who is single, can be seen wearing a wedding ring, specifically when Hogan is packing up his office so that the new senior POW can move in. (Larry Hovis refused to take off his wedding ring throughout the series, and was usually seen wearing gloves or keeping his left hand in his pocket.)
'Colonel' Crittendon is always shown as a RAF officer, but the RAF never had that rank after 1919, so he would have been a Group Captain, which is the RAF equivalent of a Colonel.
At one point, Helga asks Col. Klink if he is volunteering for "active duty" so that he might become a "war hero." Actually, Col. Klink is already on active duty. He is just not currently flying or stationed at the Russian Front.
In the introduction, LeBeau brings the Baroness (Lili) in through the entrance in the dog kennel (under the doghouse). Hogan orders LeBeau to go back up to keep lookout. LeBeau goes right back up the ladder he came down. LeBeau comes back down the same ladder to tell Hogan that Klink is looking for him. Hogan goes back up the same ladder. It makes no sense that LeBeau would keep lookout from under the doghouse, as it would be too easy to see the raised part of the doghouse. He should have gone up the ladder into the barracks. The same issue also applies to Hogan going up the ladder. He should go up the ladder to the barracks, not the doghouse, to go see Klink.