These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Are the Princes well-meaning guys with bad impulse control, spoiled by a life that has offered them no challenges at all, or sleazy, manipulative bastards who take advantage of any opportunity to get laid? Or some combination of the two? The script leaves them open to played in both ways, including anywhere on the spectrum between them. This is especially the case for Cinderella's Prince, who gets more screen time and has more impact on the story than his brother; he's very quick to jump on the Baker's Wife, but he does genuinely seem to care about Cinderella.
Rapunzel's prince can come off very differently depending upon how the actor plays his reaction to her insanity, and his reaction to her death can be played as either cowardice or grief.
Cinderella's Father. In the original production, her father seems to have selfishly abandoned her to his wife and stepdaughters (and quick to change when his real daughter gets to marry the prince), whereas the revival plays him as being "not all there," implying he simply does not realize Cinderella's situation. The film version avoids this issue by killing him off. Cinderella's Mother-In-The-Grave gets this, too. The original plays her as a Stage Mom whereas both the revival and the film version plays her lines empathetically.
The Witch comes across as much more evil in the film adaptation, to the point where Rapunzel seems like just another one of her victims than anything else.
Award Snub: Emily Blunt was expected to win the Golden Globe for Best Actress - Musical or Comedy by numerous sites. Amy Adams, who funnily enough played the Baker's wife before, ended up winning for Big Eyes.
"Last Midnight", a whole bunch of other stuff that qualifies for Tear Jerker.
"Agony" is a Funny Moment for the first act, but then the reprise in the second act is even funnier.
"Prologue: Into the Woods" is amazing onstage, but the film version is really something special. Especially at the very end, where all the different voices and lyrics come together and flawlessly harmonize and flow with each other... it's enough to drive you to tears, and for fans of the stage show, this was the first major sign that all their worries about the adaptation were for naught, and that this was going to be a good movie.
Chorus-Only Song: "Children Will Listen" actually has a short introductory verse that was not used in any of the main productions. However, it was recorded for the revue "Sondheim on Sondheim" and singers occasionally use it when recording the song on its own.
Critical Dissonance: Critics are mixed on the film but overall are leaning more on the positive side. Audiences, on the other hand, are even more mixed on the film, with a 53% audience rating on Rotten Tomatoes.
Ending Fatigue: The film version has received complaints that it really should have just been an expanded version of Act 1, especially since some of the darker elements of Act 2 are toned down anyway. Since there is no attempt of translating the story being two separate acts into film, it also loses many of the powerful parallels of structure and song.
Fan-Preferred Couple: A weird example, as Baker/Baker's Wife isn't disliked, really, but the fandom generally agrees that after the Baker's Wife dies, after some mourning, the Baker moves on with Cinderella. About 90% of the fanfiction ships them.
Family-Unfriendly Aesop: The musical added "It's probably not a good idea to marry someone you just met" Aesops to the Cinderella and Rapunzel stories. Cinderella's prince is a philanderer, whereas Rapunzel is somewhat crazy. The only original story Aesop it leaves intact is Little Red Riding Hood's Aesop of "Don't talk to strangers," who became a good deal creepier. At the end, we get an Aesop of "Listen to people who know what they're talking about, even if they're witches."
They Wasted a Perfectly Good Plot: Rapunzel being The Baker's Sister is NEVER touched upon, outside The Baker asking about her briefly at the start of the play. One would assume that since it was a major plot point for the Witch's character, it would also be something that The Baker would ask further questions about. Especially since, to break the curse, The Baker's Wife stole some of Rapunzel's hair. It also doesn't help that The Baker actually witnesses Rapunzel's death, and yet we only focus on the Witch's reaction. Had The Baker's relationship with Rapunzel been explored, it could have helped add to an already great character; instead, it all feels like a wasted opportunity. The fact that she and Cinderella are sisters-in-law is also never touched upon; it would be sweet to see them interact considering they have similar back-stories. This gets worse in the film version, where Rapunzel survives and the Baker actually does implore about her whereabouts to the Witch.
What Do You Mean, It's Not for Kids?: Oh, it's a cheery musical with all of our favorite fairy tale characters together! Then Act Two comes around, most of the characters get killed by a rampaging giant, and suddenly it's not so cheery anymore. The show has enjoyed myriad School Play productions anyway, but as of The New Tens the show's licensor now offers a "Junior" version for school and children's theater groups that drops the second act.
Plus, the message of "Children will listen" is more aimed at parents (adults).
The film adaptation, being a musical Disney film based on fairy tales. Yes, it's a somewhat Lighter and Softer adaptation of the original stage musical, but the film still ends with a rampaging giant and the deaths of major characters.
Win Back the Crowd: The first trailer for the film showed none of the singing and was met with mixed reaction among fans. Later trailers showed the singing and increased anticipation for the film.