Is she a well-meaning bookworm unfairly made an outcast by the villagers, or is she actually a snob deserving of being ostracised? She certainly wants a more exciting life than what she finds in "this poor provincial town", but at the same time the villagers turn out to be much nastier than they appear...and have no problem with holding up Gaston as a hero and supporting anything he does, including continuing to pursue her even though she's not interested. It doesn't help that the stage musical makes the "snob" interpretation more valid: The additional song "No Matter What" has Maurice actually telling her "[The villagers] are the common herd/Take my word" — which also makes him look bad.
Is her falling in love with The Beast genuine or the result of serious Stockholm Syndrome towards an abusive captor? Trying to puzzle this out will often cause an Edit War.
Is Belle experiencing a similar character arc to the Beast's, rather than remaining as static as she seems? She's the one person from a wealthy and educated family in a blue-collar town, and she's openly contemptuous of her social inferiors (who would be one step up from serfs in context, while she and her father would be petty nobility). The books she carts around alone are worth enough money to buy half of the village outright, and her father has access to machined gears while everyone else lives in basically the dirt. So does meeting the castle slaves, who are actual serfs, and being won over by them represent an actual character arc, the out-of-touch noblewoman realizing the value of commoners and learning not to be such a jerk to people outside her immediate peers? Is the Belle who is willing to give marrying a literal animal a try the same girl who previously dismissed everyone who couldn't read (a skill quite literally solely possessed by the idle rich and the clergy) as trash?
In a departure from the original story in which the Beast was kind and gentlemanly (if very rarely hot-tempered), the Disney character starts off angry and depressed and has all the classic trappings of the villain.
Commentary from the filmmakers has fueled theories that the Beast is near-suicidal for much of the film and his rescue of Belle from the wolves was also an attempt to kill himself while doing something meaningful.
When the Beast decides to spare Gaston; did he do it because Gastons words reminded him of when Belle begged to let her father go...or was he reminded of when he was cursed and how he could be offering Gaston the second chance he never got? Both sides insist their interpretation is the correct, intended one.
The song "Be Our Guest". Do the servants want to make Belle feel welcomed in the castle and be kind to her, or are they only being extremely courteous to her at dinner because she is able to change them back into humans? (Notably, the original plan was for the characters to sing this to Maurice, which would fall under the former interpretation, but the filmmakers felt it was better to use such a big number in the service of one of the leads.)
Is he a complete jerk? Is he actually a fun guy with a zest for life who thinks that Belle has been driven mad, because she seems to think that this monster is a nice guy? Is it him who winds up going mad after Belle rejects him and humiliates him in front of the entire town? It's worth noting that he was originally supposed to die by falling off a cliff and laughing hysterically, indicating that he had indeed been driven mad in his desperate effort to impress Belle.
Another interpretation: Gaston is a man too caught up in being the "ideal man" in his community that he cannot express himself outside of macho stereotypes. It should be noted that while it has the trappings of wanting what you are denied, the audience doesn't really get to see the village itself and the only other women we see are swooning and passive with Gaston. Maybe deep down, he wants the woman who is different because she will actually display a personality despite what tradition says. Unfortunately as a product of the society, Gaston regurgitates these ideals (women shouldn't read & think) because it is what his culture tells him is proper. The fact that Belle is brave enough to buck these traditions despite the pressure of their culture may be what truly appeals to Gaston deep down, as a man so thoroughly trapped by the masculine ideal. Listen to his boastful song, that is either an extremely arrogant man who is supported in his arrogance by his peers, or a deeply insecure man whose life's purpose is "to be the best" and any deviation from that would render him worthless. Ultimately, his unwillingness/inability to change/escape his such trappings, and his twisted approach to courting/acquiring what he desires (Belle) is what leads to his downfall. Not blaming the village itself, as the village showed deep adoration for Gaston, they may have changed too once he was brave enough. However, Gaston had a choice of how he interacted with Belle and he chose poorly many times. As pointed out elsewhere, in a WMG, Beast and Gaston could easily have turned out like each other if a few details were changed.
Jerk or not, it's a common interpretation that Gaston's response to Belle's situation is much more reasonable than the film treats it. He ignores the town's resident crazy at first, but when he realizes that Belle is actually missing, and that both she and her father were kidnapped by a murderous magical beast... well, he's the town's hunter, taking care of dangerous animals is quite literally his job and from his perspective he isn't forming a mob to attack a misunderstood magical loner, he's rallying the townspeople to protect an unpopular girl in danger. Magic is essentially an Outside-Context Problem that he would have no idea how to deal with.
A modern interpretation has Gaston as the kind of abusive ex who reacts to a breakup by viciously attacking the life and/or character of their former partner, and escalating their attacks as time goes on.
Perhaps the biggest one, in that it even inspired a lot of debate and even fights behind the scenes, is the question: Who is the actual protagonist? Belle is certainly the viewpoint character, and most of the story is told from her perspective, but the character who develops and changes the most as a person, and whose actions drive most of the plot, is the Beast. Lyricist Howard Ashman in particular was convinced of this, and modern critics are more and more inclined to agree.
The villagers. Are they misguided people who are genuinely afraid that the Beast might harm their children? Or are they true monsters of this film, since they're the ones who put Gaston on a pedestal and back his more devious plans? The fact that they willingly supported Gaston's plan to blackmail Belle into marrying him, despite his revealing enough of it to know how horrific of a plan it is, with absolutely no sign of fear, strongly supports that theory.