The German customs office would not allow the film-makers to bring any Nazi costumes and regalia into Germany, but fortunately the makers of Inglourious Basterds helped director Vuorensola by revealing how they had circumvented the same problem.
On a large computer screen in one scene, the "greatest war machine ever created by man", a.k.a. the "Götterdämmerung", is described in German as "eine Beförderungsplattform für duale ultra-schwere relativistische kinetische Atomhaubitzen". Literally, this translates to "a carrier for dual ultra-heavy relativistic kinetic atomic howitzers".
A tribute to 'Pink Floyd' is made by using synthesizer effects for barely a few seconds from the band's track "On the Run" from their album Dark Side of the Moon (which is where the Nazis made base). The music can be heard just after the scene where the Earth fleet departs for the moon.
The radio traffic heard in the scene where the spaceships from the other UN countries join the fight was entirely crowdsourced. The dialog were recorded by fans of the film at home and send to the director.
The Nazi moon base is located in the Schrödinger crater on the far side of the Moon. The crater is named after Austrian physicist Erwin Schrödinger, best known for the Schrödinger's Cat thought experiment.
The original idea was conceived by Jarmo Puskala in a dream. He told the director Timo Vuorensola about his dream in a sauna, and Vuorensola replied he would make it into a film only if they got Udo Kier to act in it and Laibach to make the soundtrack.
The fighter jets used by the US to repel the Nazi attack are Fairchild-Republic A-10 "Thunderbolt II" and Lockheed Martin F-22 "Raptor". The F-22 is even shown with open weapons slots when attacking the UFOs as the stealth abilities of the aircraft are greatly impaired by external weapons such as missiles and bombs.
When Adler orders the attack on Earth at 5.45 he uses the exact words of Hitler when he announced the war with Poland claiming that Germany was firing back and that "von jetzt ab wird Bombe mit Bombe vergolten" ("bomb will be retaliated with bomb").