Question: What exactly is the "cooler"?
Question: Who was "Nimrod"?
Answer: Nimrod's actual identity was never revealed in the series. It was only known that he was a British intelligence agent. Nimrod was not Colonel Klink. Hogan had only implied it was him as a ruse to get Klink returned as camp commandant, not wanting him replaced by someone more competent who would impede the Heroes war activities. The term "nimrod" is also slang for a nerdy, doofus type of person, though it's unclear why that was his code name.
"Nimrod" is originally a king and hero mentioned in the Tanach and taken into the Bible and the Koran. His name is often used in the sense of "stalker," "hunter," and sometimes figuratively as "womanizer" as in "hunter of women." I've never seen it used to denote a nerdy person, and although I cannot disprove that connotation, I think given his role, the traditional meaning is more likely the intended one.
It's widespread enough that Wikipedia has an entire section on it: https://en.wikipedia.org/wiki/Nimrod#In_popular_culture
Question: Many times Hogan and company manage to actually escape Stalag 13, especially at night. If they can escape so easily, then why doesn't everybody in the whole Stalag do it and head to an American Embassy?
Answer: The core POWs regularly escaped and returned to the prison camp because they made it their mission to conduct espionage and commit sabotage in the surrounding German territory. They also collaborated with different underground resistance groups and used a network of secret tunnels to help prisoners from other POW camps to escape, who then relayed vital information back to the Allied forces. Hogan and his men maintained the illusion that Stalag 13 had never had any prisoners escape in order to avoid their covert operations being shut down. Being that the prison camp is set in Germany during WWII, there were no American embassies.
Hogan has mentioned to different characters that they are actually stationed at Stalag 13 to help allied soldiers and prisoners from other Stalags to escape Germany.
The Antique - S5-E12
Question: When Hogan gives Klink $100 for the cuckoo clock, the bill handed over was a crisp American $100 note. How did Hogan get an American $100 note? At best, in this time period, he should only have Reich Marks. And how would he have 333 Marks, 33 pfennigs? Unless he had a side businesses going, this seems unlikely.
Answer: It's a comedy, not a documentary.
Perhaps it was counterfeit. There are numerous episodes where they deal in counterfeit monies.
Answer: Werner Klemperer fled Nazi Germany as a teenager. His two conditions for taking the role of Colonel Klink were that he had to be a bumbling idiot and he always had to lose. It would then be a character mistake that if Hogan offers him a fresh American hundred-dollar bill, he's not going to ask questions, he's going to take the deal. The fact that he's Commandant and could just confiscate the money from Hogan would never occur to him because, again, he's a bumbling idiot who, by the actor's contract, always has to lose.
Chosen answer: Hogan and his men are running a spy ring out of the camp, they have access to supplies from outside. (In another episode, they have to convince a defecting German officer that they're legitimately working for the Allies by arranging a specific personal ad to run in the next day's London Times, so a new $100 bill is not beyond their capabilities).
Answer: Rightfully, Hogan should not have any money at all. POW were stripped of all cash they carried. The intention was to make escape more difficult. The fact that Hogan has what is the equivalent of a third of the price of a KdF-Wagen (You'd probably know it as a Volkswagen Beetle) in cash should rightfully make Klink more than a litle suspicious.
Question: In this episode, Hogan and company used gold bars disguised as bricks to replace the destroyed wooden steps. However, the next episode, "Hello Zolle", the steps are back to wood. Is this considered a Continuity mistake or was it cost a cost cutting measure?
Chosen answer: It was neither of those. In earlier TV shows, it was typical that each episode was a self-contained story, and the plots and non-regular characters were rarely carried over from previous shows to the next. Any problems or situations were resolved at the end, even if some plot threads were illogically left unexplained. This allowed episodes to be aired in any random order. Today's TV series usually have ongoing linear timelines and continuous plots that are played out over multiple seasons.
Question: What season and episode was it when they had to lean the guard tower and the POWs in the camp leaned so the guards would not notice?
Answer: 1-24: How to Cook a German Goose by Radar.
Question: Why do they use gas lamps in the tunnels when they have electricity?
Answer: They would need to have access to a large amount of electrical wiring, lights, and other supplies to rig a usable lighting system. Using electricity could also drain power from the rest of the camp, alerting the Germans that something is going on.
Also. The power would go out during air raids and the like. Whereas oil could be used to stay lit no matter what (despite the fact that it uses oxygen from the tunnel and the fumes would probably kill you).
Question: In multiple episodes we see a box hanging just inside the barracks door. What is that? It is mostly blue, and appears to have flowers or something painted on it.
Answer: After careful inspection, the aforementioned box is a decorated holder for the boxes of long matches needed to light the stove.
Chosen answer: In different episodes of "Hogan's Heroes, " the arrangement of items in the barracks varies. Sometimes there is a sink on one side of the door. Sometimes there is a chest of drawers on the other. I have seen episodes where a hanging box is there, as you describe. To my eye, the decoration appears to be a kind of camouflage design. I had assumed it was where mail was delivered to the prisoners. It could also be a storage for small items, such as a medicine container. I don't recall ever seeing it opened or otherwise used. Normally, in situations like this, when questions arise regarding set pieces, set decoration or costumes, I attempt to look up the show's crew members IMDb.com to pose the question to the source (when I can find them on, say, Facebook). In this case, however, all of the gentlemen responsible for set decoration on "Hogan's Heroes" have since passed away.
I have the series on DVD, and have been able to scrutinize the blue box. It is a decorated holder for the long matches used to light the stove. Occasionally, you can see part of the word 'matches' through the slot on the side.
Question: In the episodes where Hogan or the others tell Schultz what they're planning, why doesn't Schultz report to Klink immediately and tell him? Why claim he sees nothing, hears nothing or knows nothing?
Answer: Essentially, because if Schultz reported what he saw, it would mean admitting that Hogan and his men's very elaborate schemes were happening on his watch, which would get him into very serious trouble. His greatest fear is being sent to the Russian Front, and he's in far too deep with Hogan (e.g, accepting bribes of food) to escape punishment if it all came to light. What may have started as small acts of "looking the other way" (Schultz is a generally friendly person, who may have let things slide a bit early on) has become self-preservation. For their part, Hogan et al. try to avoid getting Schultz into trouble, because if a stricter guard were to replace him, they'd come under much greater scrutiny, which they want to avoid.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.