Fridge Brilliance: when the Nazis are killed, it is during a violent propaganda movie in which a 'war hero' slaughters hundreds of Allied troops, which invokes cheering from the Nazis. However, after watching the film which is almost a parody of an American propaganda movie, a thoughtful viewer might realise that he has just watched two Allied 'heroes' slaughtering Nazis, which is almost inevitably enjoyable for your average viewer. Tarantino is highlighting the way the violence cinema in cinema brings out the worst in people, providing the violence is directed toward Acceptable Targets.
The Basterds originally start out as eight Jewish soldiers, with a ninth commanding officer. This is reminiscent of a Hanukah menorah, which has eight candles and a ninth used to light them. Hanukah is a holiday celebrating a Jewish revolt. However, the candle used to light the eight others is called a "shamash," meaning "helper," which does not groove with the soldier/commander dynamic. The Basterds are never arrayed in a way that suggests a menorah, and also gain a ninth member, which throw off the metaphor. It's probably just a coincidence.
Unless you consider Hugo Stiglitz as "the helper". He's the only non-Jewish member of the Basterds.
When Frederick Zoller gets angry at Shoshanna at the end because she kept turning him down, some people would have been surprised...but Fridge Brilliance does kick in at this point - he's a "niceguy" who honestly believes himself to be a Dogged Nice Guy, and as it goes with most real life "nice guys", they often react with anger and frustration when the Dogged Nice Guy act doesn't work. Even though he's being kind to her throughout the film, he continually refuses to get the message that she isn't interested in him, nor does it ever cross his mind that he might not be able to "win her over"; by the end of it, he realises that treating her with basic kindness and respect isn't going to get him laid, and he throws a tantrum over it. Any girl who's had to deal with a guy who's behaved like this can pretty much see how this "romance" would end right from the start.
Fridge Logic: Carving a swastika into a forehead isn't actually all that horrific, in the long run - even 1944 reconstructive surgery was capable of removing it. The victims might still have a noticeable scar after surgery, but the original shape wouldn't be visible. It's possible that Raine didn't know about that much about cosmetic surgery. Even if he did know. he might have just wanted to scare his victims.
Good luck finding a doctor who'd perform it, however, even assuming the cutting doesn't sever muscles.
Even though plastic surgery at that time was available, it would still prove to be far too expensive for a normal soldier in post-war Germany
Possible Fridge Brilliance here: in some traditions of Kabbalah, there's a belief that particularly holy people, such as Moses, have letters of the name of God (YHWH) shining from their foreheads, whereas particularly evil people have demonic signs. What Aldo's saying might not be "You'll have this (the swastika scar) for the rest of your life" so much as "You can't take this off because I'm just showing you for what you are."
While Goebbels is pretty clearly an Evil Mentor to Zoller, does anyone else notice that apparent Dogged Nice Guy Zoller seems to be taking after him? His ego is constantly swelling due to everyone's admiration, to the point that he clearly oversteps his boundaries with Goebbels (who laughs it off) and Landa (who doesn't), which is pretty telling for a mere private. Also, his outburst at Shoshanna shows a massive sense of entitlement, and his sudden return to nice guy once he gets what he wants seems to mirror Goebbels' childish mood swings.
Landa does not, in fact, strangle Bridget Von Hammersmark for treason. He strangles her because he was already planning to defect and let the Basterds kill Hitler—and already planned to cast himself in the role of the planner and hero. The role that Bridget herself had, in fact, occupied. He killed her so that she wouldn't be able to take the credit or expose that he wasn't really the mole in the Third Reich.
Fridge logic: how did no-one in the basement bar recognise Stiglitz? Landa recognised him, and it's shown in an earlier scene that not only did Stiglitz murder thirteen Gestapo officers, he was arrested and the story printed in at least one newspaper. It's highly likely that large amounts of people saw his photo, either in a newspaper or on a wanted poster. Although it's possible he was recognised and everyone chose to ignore it, that's highly unlikely.
Everyone in that bar was either drunk or just not looking at him. People tend to not see what they don't expect to see anyway. Stiglitz probably doesn't look that different from a whole lot of German soldiers either, come to that.
If Major Hellstrom recognised Stiglitz, then it's likely he just didn't want to cause a fuss with that many people present.
Its obvious that Landa speaks fluent French, English, German, and Italian. So why does he insist on switching to speaking English with Monsieur Lapadite, using a the paltry excuse that 'His French is running out'? because, as he later remarks, the people underneath the floorboards don't speak English. He switched to English right about the time he went from a pleasant milk based conversation to one that involved Jews and hiding places.
Fridge Horror: If everything goes 100% ideal in the aftermath of Operation Kino, and the European Axis (Germany, the Italian Social Republic) capitulates, then America gets to turn around and throw massive quantities of men and material that would have been committed to the Western Front at the Pacific. Good news for the Chinese in Manchuria, bad news for the Americans, because they are going to be at Japan's doorstep ahead of schedule and before Little Boy and Fat Man are ready to drop. In other words, America would go forward with Operation Downfall, the invasion of the Japanese Home Islands, which had a fatality estimate in the Megadeath range, would likely end up depopulating large areas of Japan, and could have involved chemical weapon attacks on both military and civilian targets.