Acceptable Targets: The Basterds call all German soldiers "Nazis" and seem to take glee in killing them. In reality, not all German soldiers were party members. Tarantino has claimed that he intended some of the Basterds' actions to be morally ambiguous, and most of them are outright war crimes. In general, there's no clear consensus on whether the audience is supposed to fully support all of the brutal actions taken against the "Nazis."
Of course, Sgt. Stiglitz is meant to be an aversion of All Germans Are Nazis—which the Basterds make sure to acknowledge. This would seem to imply they're taking a "you're either with us or with the Nazis" mindset towards the German military.
Also, Fredrick Zoller. Is he the Dogged Nice Guy trying to help out his crush, only to get manipulated and shot over it? Or is he a creepy, annoying Stalker With a Crush, hounding Shoshanna (a woman who repeatedly shows that she has no interest in him), believing that due to his fame, he is entitled to get whatever he wants? His last scene where he yells and threatens her after getting fed up with her attitude lends credence to the latter interpretation, but on the other hand, some of his lines seem practically lifted from a cliched romance, and Tarantino has stated that, in any other time, they probably would have ended up together. Or is he a traumatized soldier trying to get away from his dark past through Shoshanna, and watching himself kill repeatedly pushes him over the edge?
Bridget's motives in aiding the Allies are never stated, they could plausibly be anything. Is she a courageous and committed anti-Nazi? A bored actress who became a spy for the kicks? A pragmatic, female version of Landa who is trying to secure a life for herself in the inevitable Allied victory?
Losing Best Original Screenplay to The Hurt Locker. It also lost Best Picture, though it wasn't the favorite. Given the director involved many expected him not to walk away with an Academy Award anyways. Though he won for Pulp Fiction and would win again for Django Unchained.
Other than Christoph Waltz, many found the best performance in the movie to be that of Melanie Laurent's Shosanna, who was nominated neither for Best Actress or Best Supporting Actress by the Oscars, despite some thinking she would've easily been a Top 5 contender either way.
Diane Kruger was also nominated for a SAG Award for Supporting Actress that failed to translate to an eventual Oscar nod.
Shosanna Dreyfus, hands down. Risking everything to execute an attack on the Reich and actually going through with it, even though it costs her her life - while wearing red dress and putting on war paint to David Bowie.
Do Not Do This Cool Thing: Lampshaded in a subtle, creepy way: there is a scene where Germans are watching a Nazi propaganda movie about a German sniper who killed massive numbers of Allied troops while behind enemy lines. They are laughing and enjoying themselves watching people from our side get slaughtered, while you're laughing and enjoying yourself watching people from their side get slaughtered. However, some audiences even laughed and hooted while the allies were being slaughtered. Laughter, she is an infectious drug, is she not? And the funniest part is that both reactions were probably predicted and intended.
Michael Fassbender's next big role after this was as Magneto in X-Men: First Class. And when we catch up with the adult Erik Lehnsherr in that film, he's doing one thing and one thing only — killing Nazis.
The Basterds did what Danger 5 could not: kill Hitler!
Daniel Brühl would later be cast in Captain America: Civil War as Helmut Zemo, a comics character who traditionally has strong Nazi ties as part of his backstory (though this element was not carried over into the film).
Ho Yay: When Hitler congratulates Goebbels on Nation's Pride, he addresses him as "my dear." Goebbels is so overcome with emotion at hearing this that he begins to weep.
Magnificent Basterd: Hans Landa is a possible example, as he gets personally involved in many of his Gestapo investigations and ultimately takes a huge risk for personal glory. He ALMOST gets away without a scratch (and what a scratch it is!).
The Basterds, together with Indiana Jones and Captain America, have become mascots for those who celebrated when a masked man punched self-proclaimed white supremacist Richard Spenser in the face on live television on January 20th.
NEIN, NEIN, NEIN!
Which leads to a counterpart memetic joke: "What is Hitler's phone number?" (Think about it....)
Zoller, when he finally snaps and shows that he doesn't take no for an answer. If he did not, Shosanna shooting him in the back probably would've been too contemptible, even for a movie such as this one. However, some view him as just a man with a misguided crush. This interpretation is supported by Word of God: Daniel Bruhl describes his character as a straightforward Dogged Nice Guy: "He's sweet and he's handsome... He has to fight hard to get Shosanna, and he does so throughout the film". Quentin Tarantino adds: "Everything Zoller did that ended up fucking her up and putting her in this situation, he did with good intentions. His biggest crime was liking her". One could also add "and not accepting that she didn't like him back". In all his passiveness and decent manners, he was very much a coercive stalker from the start.
Our introduction to Donnie is witnessing him mock, berate, and brutally beat to death an unarmed German prisoner of war on his knees who courageously refuses to betray his comrades. The sadistic war crimes committed by the Basterds cements their role as significantly more villainous than the average German soldier, despite being the protagonists of the film. You might consider that the beating was more a show to scare the last survivor into giving up information that they knew the officer wouldn't give them than sadism for its own sake (or in addition to sadism for its own sake more likely).
Landa's murder of Van Hammersmark. Given the timing, he has probably already decided to go along with the Basterds' plot, and even if he hasn't, there's something particularly brutal with the way he personally strangled her to death. His earlier actions, deplorable as they were, were borderline Punch Clock Villainy, but this was darker. Then again, Landa's actions, like the massacre seen at the beginning of the film WERE very much his own choice. While they were started and orchestrated by Hitler and Goebbels who were obviously gone long ago, as Landa himself admitted he hunted people and Jews would be the target that guaranteed more personal power, without actually believing in all that Jewish propaganda crap.
Neutral Evil: Col. Landa aka "The Jew Hunter" would appear to be Lawful Evil but has a chaotic streak: choking von Hammersmark to death, letting Shosanna live on a whim and ultimately selling out Hitler to save his own skin and being richly rewarded by the US government, landing him here.
Periphery Demographic: One thing Quentin Tarantino and Eli Roth didn't expect is the movie having such a large popularity among the yaoi fans. Though they both announced their immense approval of the fan fiction upon discovering it.
Propaganda Piece: Goebbels' film is a glorified account of German sniper Zoller killing Americans.
Ships That Pass in the Night: Donny/Utivich, one of the fandom's most popular ships, even though they exchange no dialogue. It's still possible because we only see a little of the Basterds and they probably had a lot more contact with each other than what is actually shown (a good reason to hold out for a prequel).
Trailers Always Lie: Much of the marketing campaign focused solely on the Basterds and Landa, giving off the impression that the story's about them. While they are main characters, Shoshanna and her role in the plot are just as important and she's nowhere to be found in the trailers. Possibly justified as Mélanie Laurent was virtually unknown to American audiences at that point.
The whole fiasco in the tavern could have been avoided had the Basterds: a) chose their meeting place as somewhere not crawling with Nazis; b) not had Stiglitz, a former Nazi officer and wanted criminal, impersonate a Nazi; and c) just told the officer, "Do you mind, we're having a private meeting?"
Shosanna's reaction to Zoller stirring after getting shot by her. She leans in close to check on him, as if in remorse. She gets blasted.