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.
The classic princesses—Snow White, Cinderella, and Aurora—are often criticized in fandom (and media) that believes they are terrible role models, boring Mary Sues, shallow characters, and bad examples of feminism. Alternatively, many others see them as having perhaps aged not quite well, but still good characters that were limited by the time period they were in.
Ariel. Fans are a bit divided on whether she's "an idiot for throwing her life away to be with someone she doesn't know" and should be regarded as poorly as the previous three Disney Princesses (who haven't aged well), or she should be commended for being "the first Disney female lead to have an actual personality and be the one to save her prince first."
In a similar pattern to Ariel, Merida is criticized for her impulsiveness and general teenage attitudes. Some find her to be refreshingly normal and realistic for her age as well as a certified badass, others find her to be just an insufferable brat with a remarkable callous streak.
Broken Base: Over the inclusion of characters who do not seem to fit with the line as easily as characters like Aurora or Rapunzel; that is, Pocahontas, Mulan, and Merida for being too athletic, not girly enough, and/or not a princess.
Critical Dissonance: Despite its critics, the franchise is one of Disney's biggest and most profitable.
Girls Need Role Models: Initially why the line-up was created—certainly all of them are in possession of admirable "role model" traits. This is generally how Disney defends the inclusion of non-princesses Mulan and Pocahontas, as well, citing that its their quality of character that makes them a Disney Princess.
The Disney Princess design of Merida had multiple issues people drew from it:
First, fans perceived the dress to be entirely new, a "girly" version of the adventurous gown she wore in the majority of the movie. This is not strictly true, as the dress is actually a version of what she wore at the very end of the film, albiet more sparkly.
Second, was the cut of the dress. There was back-and-forth regarding whether the neckline was lowered.
Third, whether she was posed to look seductive or not.
Lastly, any changes to Merida's face and body, which was the most contentious. One the one hand, some people were claiming she was paler, appeared to be wearing make-up, her hair was more stylish than wild, had features altered to seem more attractive, and that her breast/waist ratio got wider. On the other, some people felt that much of that was simply a result of the 3D-to-2D transition. Still, there was no getting past Merida's waist getting thinner.
Periphery Demographic: The merchandise is aimed at young girls, but if they aimed for males adolescent and older, they might find an audience there as well, as long as it's subtle enough to avoid setting off moral guardians. There are also plenty of female fans in their teens or older.
Tastes Like Diabetes: The extra merchandise and sequels are loaded with saccharine morals, songs and messages that tends to be unpalatable to anyone but very young girls.
Testosterone Brigade: The especially Ms. Fanservice characters—Ariel, Jasmine, and ostensibly Pocahontas—invite a lot of male fans, but many little boys grew up with crushes on one of the princesses that stuck.
Many of the girls coloring and style is changed for the merchandise, such as Aurora's lighter hair, Cinderella's dress changing from silver to blue, her hair changing from strawberry-blonde to bright blonde and so on.
Aurora and Tiana graced the wrappers of some dipping candy. Aurora got the packet of vanilla-flavored sticks. Tiana got the packet of watermelon-flavored powder.
The new designs attempted to homogenize the general look of the Disney Princess line and the different art-styles, which led to everyone either getting paler or darker, the brightness being turned up to max, and some of the efforts to make the art seem more detailed really failed to the point where dark-eyed characters seemed blue-eyed. The homogenization of art style, however, led to the faces looking more Caucasian than anything.
Values Dissonance: One justification of the Real Women Never Wear Dresses criticism. Not only were the original fairy tales written centuries ago, but the time periods in which the earlier Disney Princesses were made had the "demure-but-hard-working" type as the epitomy of womanhood in mainstream America. Naturally, this flies up the head of many modern fans who just peg them as "weak" and "whiny".
All of the Disney Princesses are treated as such. The older princesses receive the most disdain, as the time period their movies were made from put them in the passive role that would not be acceptable in a female role-model today. Even the modern princesses are often closely scrutinized and found unworthy, particularly Ariel. While there is some truth to the criticisms, the biggest criticisms lobbied at the girls tend to twist the actual events of the movie. For instance, the common criticism that Ariel gives up her life at home for a man isn't exactly true—Ariel clearly desired to live with humans long before she knew who Eric was, he just was the catalyst to actively going out.
Disney draws a lot of ire from the older fans when Mulan is put in a feminine dress (particular the pink one with make-up that she felt uncomfortable in). However, as with the above case, even those criticisms are often twisted—Mulan is also clearly uncomfortable wearing armor and hiding herself that way, and did like looking cute in the pink dress even if she disliked the prospect of an Arranged Marriage. The happy medium is usually the far more practical (and plain) dress she wears at the end of the film.