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 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.
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 scene in which Vivian Wagner is at her public relations firm going over her staff's presidential campaign pitch is a direct parody of the scene in Downfall (2004) in which Hitler discovers he'll lose the war. Peta Sergeant even shakily removes her glasses the way Bruno Ganz as Hitler does in the earlier film.
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.
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".
The sound of a bell tolling is played repeatedly while the Nazi flying saucer is on its way to Earth on its first mission. This seems to be a reference to modern Nazi/UFO Mythology, which alleges the existence of a secret SS project to develop a machine known as "Die Glocke" - the Bell - an anti-gravity device designed to power the (fictitious?) "Haunebu" - the secret Nazi saucer. The saucer shown in the film also strongly resembles the "Haunebu" as depicted in various images claiming to depict this craft.
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.
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").
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.
Vivian Wagner's first scene with her campaign staff is a homage / parody of the infamous scene in the German movie "Downfall", which is a popular internet meme where people add arbitrary subtitles to Hitler's berating (in German) his staff in a bunker.
The scene where Washington, after he has been "albinised", is trying to respond to the Nazi salute while in a wheelchair is a nod/parody to Stanley Kubrick's 'Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb (1964)'.
Götz Otto: In addition to playing Klaus Adler, he has a cameo as a mustached campaign designer in the scene parodying Downfall (2004). Otto was in the original scene and perfectly mirrors his original role.
Johanna Sinisalo: The writer credited as having the original idea for the film appears as the candidate running against the president in the upcoming election. Seen in the news feed in the start of the limo scene.