Many people (including Meg Cabot) seem to overlook the fact that Michael not only helped Judith Gershner cheat on her boyfriend but also "jokingly" told his much younger girlfriend that he "wasn't going to wait forever" for them to have sex. Though it was mostly in the context of Mia wanting to have sex when they went to join Greenpeace protest ship instead of attending collage. He wasn't demanding to have sex immediately and refuses sex when she offers.
Similarly, J.P. points out several of Lilly's faults, including the ways she mistreats Mia. We are later supposed to attribute this to J.P.'s Manipulative Bastard nature trying to pit Lilly against Mia, but his points are valid. Tina also points them out more gently, namely about Lilly getting Green-Eyed Monster about Mia getting attention from guys.
The entire Lilly/Mia conflict in the final books is divisive. Was Mia too self absorbed to notice Lilly's pain, or was Lilly irrationally blaming Mia for something that wasn't her fault?
Angst? What Angst?: Olivia is remarkably emotionally stable for a child who's been treated the way she has. She also handles the abrupt changes in her life, including having to move across the world, with little-to-no trepidation.
Author's Saving Throw: Following Lilly's Disproportionate Retribution over JP breaking up with her to date Mia, and Mia being oblivious which a good number of fans commented on, she gets Demoted to Extra in Royal Wedding though she does play a small role. Also, while Mia gets Lilly back as a friend, they aren't as close as they used to be, and Lana was a much better friend to Mia during their senior year.
Ensemble Darkhorse: Lilly in the films. Not so much in the books where the Darkhorse is Tina.
Book example: Michael insists that Mia has to have sex with him in order to be a true girlfriend. She eventually gives in. When she walks out on him before they can do the act, even her PARENTS say that she did the wrong thing. The only guy who stands up for her decision turns out to be an inadequate boyfriend for her. Eventually she reconciles with Michael because First Guy Wins. The moral of the story? If you love him, sleep with him, even if he's fooled around with girls where it 'didn't mean anything' and he's being manipulative about the issue of sex and YOUR RESPECTIVE AGES MAKE IT STATUTORY RAPE.
Mia has an extremely romantic view of sex wanting to skip college and go out on a whaling boat with Michael to have sex. She also has the idea of a romantic prom night deflowering that fails to account for her emotional state at the time. This didn't work out when JP tried it. Her mother and Michael both call her out on it and Michael claims that he would like to have sex at some point as part of their romantic relationship. Which is totally normal and reasonable. He actually refuses to have sex with her when she tries to use it to manipulate him because he thinks she isn't ready.
It's not clear whether Mia told her dad that she had been planning on having sex. She explicitly says that she did not tell her mom, because her mom would be mad at her about using sex for manipulation. No one tells her she should have had sex. Some reactions could still be filed under Family-Unfriendly Aesop: her parents tell her that she is being too hasty in breaking up with him over having had sex before and not telling her, and Tina tells her she should talk to Michael and maybe give him another chance. Lilly calls her out on judging him for having had casual sex and on trying to manipulate him into staying, both of which are fair. Boris is the one who delivers an unquestionably Family-Unfriendly Aesop: a messy breakup without closure that leaves both people miserable is better than the potential of a long distance relationship.
"Funny Aneurysm" Moment: Mia's Wangst about Lars becoming her unwanted bodyguard in the first book seems naive compared to her summoning a Royal Genovian Guard posse for her half-sister Olivia, to protect her from Annabelle Jenkins. The guard completely fails to protect Olivia due to Annabelle's father, an Amoral Attorney, tying them up in red tape.
The books, mainly due to the cultural references, can veer into this. Like in the second book, where it's mentioned that Beverly Bellerieve is sitting in front of the World Trade Center for Mia's interview.
Lilly creating a hate site featuring footage from Mia's school would get her in a heap of more trouble now, given certain hate sites have led to people getting Driven to Suicide, and to cyberbullying laws being made.
Jerkass Woobie: Lilly becomes this in Book 10, after revealing that J.P. slept with her and dumped her specifically to date Mia after Mia and Michael broke up. Mia even says that while J.P.'s terrible behavior doesn't justify Lilly's actions, it makes them understandable.
Magnificent Bitch: Grandmere borders on this sometimes. At one point she puts on a school play to help Mia raise money enough to save the student government, ensure her own purchase of an island in Dubai, and get her granddaughter closer to a boy she thinks is more suitable consort material. She succeeds on all counts.
Mary Sue: Olivia is remarkably well adjusted for growing up in an abusive household, is sweet and kind despite it, and is incredibly intelligent and creative. She's beloved by all, the notoriously difficult Grandmere takes to her within seconds of meeting her, and doesn't force her to undergo a makeover because she's perfect as she is. She even ends up solving the Genovian immigration crisis in seconds, that left most adults scratching their heads.
Take That, Critics!: Meg Cabot has long gotten flak for putting pop culture references into her books. In Princess In Training, Mia struggled with an English teacher who disparaged her for the same thing, resulting in the novel's CMOA in which Mia calls her on her overly-rigid view of what constitutes "culture."
Wangst: Mia veers into this at times. Possibly justified in that the story is written from entries in her personal journal, and it would make sense for her to be inwardly over-dramatic. (This trope is the source of several Funny Moments in the series.)
Michael never telling Mia that he wasn't a virgin, while wanting to have sex with her while she's underage. Given Mia is a health freak, telling her right when she was about to initiate their first time was the worst possible mistake he could make in ruining their relationship. While Mia blames herself for acting immaturely to the news and breaking up with Michael, Michael admits that she was right to call him out for it.
JP dating Lilly to get closer to Mia, with Lilly falling in love with him and telling him so. When he does break up with her once Mia is available, he makes the mistake of telling her that it's to date Mia to her face and gambling that Mia's Accidental Kiss of him would make Lilly too angry to inform Mia of what he said. When Mia learns the truth, Beware the Nice Ones doesn't cover it. Mia immediately breaks up with him and gets his upcoming play cancelled, and Michael nearly turns JP into a "Cream of Wheat".
Similarly, Lilly not telling Mia what happened, creating a hate site about the Princess instead and severing ties. She admits later on that she was "psycho" about it, but if Lilly had simply told Mia, Mia would never have tolerated JP's flirting and their friendship wouldn't have suffered such a rift.
An even bigger example is the scene where the maids attempt to distract the Grandmother for the Princess... by singing "Frère Jacques", dancing, putting pots onto their heads, and then taking them off and clanging them together while singing, "DING DANG DONG! (clang!) DING DANG DONG! (clang!)" Its absolutely surreal in its own right, comes out of nowhere, its never discussed again, and seems so random and out of place that the sheer "WTF face" shown by Julie Andrews is mimicked by everyone in the audience who sees that scene.
The Guy-on-Guy Is Hot moment in the sequel, which seems to be inserted for no other reason than to deflect criticism with a pro-gay message.
Crowning Music of Awesome: Quite literally, at the end of the second film; the Genovian national anthem, which had been somewhat silly in the first, becomes a stirringly performed, patriotic, and indeed almost profound piece of music as Mia is crowned queen.
Don't Shoot the Message: As The Nostalgia Critic pointed out, the pro-gay message in the sequel seemed not only shoehorned in to deflect criticism of the movie (not that this stopped most critcs)note "We're pro-something, that'll distract from the fact that we're saying nothing funny!", but it also acts as if not being homophobic in and of itself is worthy of praise.
Family-Unfriendly Aesop: The movie seems to believe that Beauty Equals Goodness - no matter how strong or intelligent or charismatic Mia is, she must look like a supermodel at all times or she isn't worthy of having authority or being noticed. Note that the villains in the first film are hideous and the film makes sure you're aware of it.
In the books, Mia points this out and mocks the movie creators about it.
Fridge Horror: Mia is fifteen years old in the film. The newspapers published pictures of a semi-nude fifteen year old and another of the same girl getting forcibly kissed.
Paolo: I love your eyebrows, I shall name them Frida and Kahlo. If Brooke Shields married Groucho Marx, the kid would have your eyebrows.
In the second film, Lilly calls Brigitte and Brigitta Rosencrantz and Guildenstern.
Hilarious in Hindsight: The part with Prince William in the second movie becomes all the funnier once the Royal Wedding comes to mind.
In The Princess Diaries: Royal Engagement, when Chris Pine's character is shown the "easy way" to win at darts, he objects with "That's cheating!". Cue Kirk and his approach to the Kobayashi Maru scenario in Star Trek...
Stan Lee's cameo in the second film, which actually predates Disney buying Marvel.
Also in Royal Engagement, Chris Pine's character is referred to as "an almost-Prince Charming" at one point. In the 2014 film version of Into the Woods, Pine plays the Prince Charming.
Lord Nicholas from the second film is played by Chris Pine, who would later shoot to stardom as Captain James T. Kirk in the rebooted Star Trek film series, and, to animation fans, Jack Frost in Rise of the Guardians
Unnecessary Makeover: Dovetailing with the Family-Unfriendly Aesop, the Hollywood Homely Mia has to get a makeover because she has glasses and a ponytail curly hair. On the other hand, she's clearly unhappy with her appearance until her makeover. And bear in mind, her makeover was more suited for a public figure than a high school student. It also doesn't help that, as Kevin Murphy put it in A Year at the Movies, the primary result is that she's "de-ethnicized," with every trace of Jewish heritage covered up.