Colonel Klink mentions that "U.S. Air Force" (known at that time as "Army Air Corps") sheet music that Hogan brought him is in the key of C. The music is actually played in the key of F.
Anyone who knows music will know that any work can be transposed into other keys. While the work was originally written in F major, a search on the Internet will find the sheet music written in E-flat major, A major, B-flat major, G major, and even C major. C major is the easiest key to play it in while A major is the most popular version. It is therefore possible that the version that Hogan brought with him was, in fact, written in C major.
Anyone who knows music will know that any work can be transposed into other keys. While the work was originally written in F major, a search on the Internet will find the sheet music written in E-flat major, A major, B-flat major, G major, and even C major. C major is the easiest key to play it in while A major is the most popular version. It is therefore possible that the version that Hogan brought with him was, in fact, written in C major.
When Klink plays 'Off We Go Into the Wild Blue Yonder' on the violin at the end, the fingers on his left hand, which select the notes, are not moving.
During the course of the meeting, several shots of the recorder are shown as the meeting progresses. The recording arm should have moved toward the center of the record as the meeting progressed, but it stayed in the same place in every shot while the record was spinning. There are two possibilities: Either the recorder was a prop and always stayed in the same place, or the same clip was used for every shot.
A production light is reflecting in Klink's monocle in some scenes.
When the 'clothesline' wire is set up, Carter brings the wire up through the tunnel and gives it to Baker to attach to the amplifier. The SS guards then bring the wire (and clothes) back to the prisoners in the barracks. When the SS guards took the wire down, they would have seen that it goes into the barracks and traced it to the end - and found the tunnels and everything.
When the SS guards bring in the wire running from the prisoner's barracks to the Recreation Hall, Baker is leaning on the amplifier in the stool. It is in plain sight, yet the SS guards never even notice it. Even the officer that held the door open does not appear to see it, even though he is looking almost directly at it.
When Klink opens his office door, a man in uniform is seen at Hilda's desk, rather than Hilda.