That's No Lady, That's My Spy - S6-E17
Revealing mistake: When the men are in ranks for roll call, it's snowing heavily. Given the pitch of the barracks' roofs, there shouldn't be any snow sticking. Therefore, if looked at closely, it can be seen that the "snow" on the roofs is painted in place.
To Russia Without Love - S6-E18
Revealing mistake: As the motorcycle and the side car split apart and drive around independently, you can see that the side car has been given two extra wheels, and some other stuff underneath as well that's not present on regular Wehrmacht BMW sidecars - probably a remote control of sorts. Also, the motorcycle Schultz rides has training wheels mounted in the shot where the side car comes off.
Klink for the Defense - S6-E19
Continuity mistake: General Burkhalter is eating Klink's dinner. When finished he places a metal cover over the plate. In the next shot the cover is lying on the table and there is extra food on the plate. (00:15:25)
Klink for the Defense - S6-E19
Factual error: About 8 minutes into show, Major Hochstetter asks Schultz how long Colonel Hogan (an American) has been running the camp, and Schultz says 3 years last November. This is impossible. The US didn't get into the war until December, 1941, He would have to have been captured November '42 or earlier but the war was over by November 1945.
Suggested correction: Not necessarily. Quite a few Americans served with the RAF before America declared war. The Eagle Squadron American volunteers fought at the Battle of Britain in 1940 for example.
Klink for the Defense - S6-E19
Visible crew/equipment: As Newkirk and Hogan enter the office, the shadow of the boom mic plays on the wall.
The Kamikazes Are Coming - S6-E20
Factual error: When Hockstetter shows up in Klink's office he has two SS soldiers with him. One has a coat on with a general's rank insignia.
The Kamikazes Are Coming - S6-E20
Revealing mistake: As the rocket blasts out of the recreation hall, the guide wires for the model are visible.
The Kamikazes Are Coming - S6-E20
Other mistake: As Marya comes out of camp office, the seams between the sections of the studio flooring are visible at the bottom of the shot.
The Kamikazes Are Coming - S6-E20
Continuity mistake: When Otto and the Russian go to leave there's another man with a blue hat by the door. When the angle changes, there's suddenly a German guard standing behind him.
Plot hole: Five minutes into the show, Klink and Hogan are in Klink's office when a gestapo major comes in. When Hogan leaves, Klink mentions Hogan's name and the major realises with surprise that that is Hogan and then says he knows all about Hogan and his description. That alone should have led the major to know that this was Hogan. Hogan also has his name on a tag on his jacket.
Plot hole: Hogan has his men play romantic music over the radio. Earlier they were afraid of the radio in the observation post being detected. Elsewhere in the series, they try to avoid sending too long to avoid being homed in on - which is correct. Now, if they were to play a whole record at once, wouldn't the homing devices pick up on the transmitter at the camp?
Suggested correction: It is shown several times in the series that the detectors are brought out at specific times / events. With how much control they have over the camp they would know when those times were / more than likely be able to tamper with them. The other times they were worried were simply because either A. They were close to the scanning times or B. New ones got shipped in that they didn't have time to tamper with yet.
Factual error: Frankel suggests manipulating the missile's gyroscope, and Hogan suggests an electromagnet as means to do it, which is later implemented. Gyroscopes however are not affected by any magnetic force, which is what makes a gyroscopic compass superior to a magnetic one in many situations. To enhance that effect, gyroscopes are deliberately built out of materials with as little magnetic susceptibility as possible. A large electromagnet next to the missile could potentially cause all kinds of havoc with all kinds of parts of the missile guidance and control, but the gyroscope itself would not be among them.