Alternate Aesop Interpretation: A video analysis states that the film can be seen as a take that against hustle culture, capitalism and commercial greed which were issues plaguing Japan from the film's release to present day, if the widespread knowledge of Japan's poor working conditions combined with the need to conform are anything to go by.
The theory that Yubaba and Zeniba are the same person. This is only applicable in the English dub. In the original Japanese version, Yubaba is much more vindictive and sinister, and has no intention of willingly releasing anybody who's under her power.
Chihiro and Haku's relationship and the nature of it is up in the air. She has a deeper connection to him than she does with the other friends she makes throughout the film - and The Power of Love benefits him far more than anyone else. But as they're so young, Chihiro never treats Haku as anything more than just a friend, so they could entirely be platonic.
Is Zeniba's role in the spirit world to act as an Aesop Enforcer? The collection of friends learn something while at her house - Chihiro learning about The Power of Love and Boh learning to become more independent. No-Face meanwhile still hasn't learned his lesson, so Zeniba makes him stay with her so she can teach him. She doesn't need to do the same for Chihiro and Boh because they already learned their own Aesops.
Awesome Art: As is to be expected of any movie by Hayao Miyazaki, the film's animation is nothing short of gorgeous.
Broken Base: The English dub inserts one final line from Chihiro saying "I think I can handle it" (re: moving to a new house). Word of God is that she doesn't remember any of her experiences in the spirit world, so fans are split over whether this line undermines that. It also means they can't decide whether Chihiro does in fact remember everything or forgets but still keeps the Character Development anyway. Unlike the lull-filling in Disney's dubs of Castle in the Sky and Kiki's Delivery Service, neither Disney nor GKids removed this (or any of the dialogue Disney added) from any DVDs or Blu-Ray Discs.
The Radish Spirit. Somehow, being The Speechless is part of his appeal.
The Sootsprites are a fan favorite, as always (basically little black balls of fluff with googly eyes).
"Oy, oy, oy, oy, oy, oy, oy, oy, oy, oy!" (Yubaba's three "Kashira" aka the three green heads.)
Fanfic Fuel: About half of the Spirited Away fanart and fanfiction department usually involves Chihiro being reunited with Haku an indefinite amount of time after the end of the movie and/or Chihiro returning to the spirit world.
Germans Love David Hasselhoff: The film is just as widely beloved and popular in the United States as it is in Japan, to the point that it recieved an Academy Award for best animated film, the only Ghibli film to have gotten one.
Hype Backlash: For some people. The film is often lauded as the greatest animated film of all time, and almost always the best Studio Ghibli film. For a time, it boasted a 100% rating on Rotten Tomatoes, which is an extreme rarity. While it's very difficult to find someone who hates the film (it's hard to find someone who dislikes it, for that matter), a few will say that it doesn't fit the "Absolutely Perfect and Nothing is Wrong with It" label that is often given to it.
Jerkass Woobie: Chihiro seems to be a bit of a spoiled and selfish brat in the beginning, but her parents are unsympathetic and dismissive of her plight, she's lost in a completely new world, where her humanity makes her an outcast to most of the spirits who inhabit the place, and she finds herself under contract from a ruthless businesswoman who's not willing to let her go.
Narm: While Chihiro crying and eating a rice cake is definitely a heartbreaking scene, Chihiro's tears are so comically large, that it can be hard not to crack a smile.
The environmental Aesop is heavy handed sure, but it shows the negative effects that pollution can have, not to mention the amount of work it takes to fix even the smallest amount of environmental damage. Hayao Miyazaki specifically wrote the river spirit scene based off a moment in real life where he was part of a clean-up crew and a bicycle was fished out of the river.
You can't buy someone's affection. No-Face thinks he can simply offer Chihiro gold and it'll make her love him. But at the same time, someone with that thinking is a product of their environment, and can still learn from their mistakes.
Squick: Studio Ghibli has a thing for animating goo and it shows! The fluid 'Stench Spirit' (and his slime trail) and the horrible effects that the purgative has on No-Face are meant to produce that reaction and they succeed! Also invoked with blood: Haku's injuries produce a lot of blood and it gets everywhere.
Ugly Cute: Some of the bathhouse spirits, particularly the Radish Spirit. *squeak squeak squeak*
Uncanny Valley: Many of the spirits have proportions that are just wrong. The effect can be rather unsettling at first. Lin, for example, looks completely human, but the frog spirits (like the head of the bathhouse, not the green one) look like humans with distorted features.
Unintentionally Sympathetic: Chihiro is meant to be written as a brat who doesn't appreciate what she has in the beginning until she loses it. Except . . . she's moving to a new place against her will, and the worst she does is whine about how she's gotten a goodbye bouquet from her best friend, whom she's leaving behind. Then when her father gets them lost in the middle of the woods, she senses something isn't right with the abandoned amusement park and yells at her family to leave. It turns out she's Properly Paranoid about that given the food there turns her parents into pigs.
Values Dissonance: A more western audience might find Chihiro's behavior a bit more understandable, given that she's pretty young and her parents constantly downtalk her. Even in the scenes where she is in the "theme park" and is telling her parents she wants to leave, she comes off as the Only Sane Man.
There is also the fact that Yubaba complains that Chihiro doesn't have a day of work under her belt. Despite technically being true, in an age with prominent child labor laws that Chihiro clearly doesn't match the age range for, it's easy to brush off Yubaba's words with the matter of the fact that Chihiro legally isn't allowed to work. Though considering she is working among presumably immortal Youkai and Kami, this could be a product of Culture Clash and is thus Deliberate Values Dissonance. It could also imply Chihiro doesn't do any chores at home, which is a reasonable expectation for children in both eastern and western cultures for a girl her age.
What Do You Mean, It's for Kids?: For a film aimed at young children, there's an awful lot of blood and other potentially frightening imagery, especially considering it was released in the U.S. In fact, it was rated PG in the States for the frightening scenes that occur since it might be a bit much for young children.
Yubaba is the only character in the bathhouse who wears a European style dress, while everyone else wears traditional Japanese attire. She also mainly cares about money and figures. This is suggested to be a metaphor for how traditional Japanese values can get lost due to influence from Western capitalism.
It's been suggested that the bathhouse parallels a child entering the work force for the first time. Chihiro is separated from her parents and must learn to get along without them, she must keep different hours than the ones she's used to, and her hard work is rewarded with gifts that help her out.
Haku, who lost his home when his river was filled so apartments could be built, then loses his name to Yubaba and is forced to become her lackey after she puts a black slug in his belly to control him.
Chihiro, too, the poor girl didn't ask to get cooped up in the spirit world with a bunch of strangers after her parents get turned into pigs!
Woolseyism: As mentioned above, the Disney dub is high quality, but there are some things that Disney thought needed to be explicated, so a few things are left out that either become more obvious in the Japanese version or were changed in the English to fit in. These changes aren't necessarily bad, and some people prefer them, but they are different.