When Newkirk is directing the new escapees he is shown smoking a long cigarette. When the last escapee walks past Newkirk his cigarette is now gone. Since cigarettes are a rare commodity during the war it is doubtful he threw the cigarette away only half smoked..
The gray in Colonel Klink's sideburns changes from barely gray to extremely gray and back again in different scenes.
Hogan tells Klink about the escape from Stalag 5. Hogan, being a prisoner at Stalag 13, would normally not be informed about escapes from other prison camps. Update: Hogan also indicated he heard about the escape from some prisoners transferred from Stalag 5. Note that Klink does not dispute that there have been prisoners transferred from Stalag 5, so Hogan's claim is entirely plausible.
In some scenes, there is a reflection of production lighting in Klink's monocle. Update: At the end, Klink says, "Hogan, you told me I would never hear from him again, and you were right." Right after this, Klink takes a bite of caviar, and flashes a full reflection of the light in his monocle.
In this episode, Schultz says that Klink raised him from a Private. In another episode, Schultz was a sergeant fighting in WW I.