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.
Author's Saving Throw: From the previous series, no less. Nico's actions toward Percy in The Battle of the Labyrinth seem much less like a hastily Subverted Create Your Own Villain subplot and much more representative of his romantic feelings after reading The House of Hades.
Awesome Art: Some of the cover art looks really, really nice. Particularly The Mark of Athena and The House of Hades.
Critical Research Failure: Minerva was in fact a very important and powerful goddess in the Roman pantheon. She formed the Capitoline triad with Jupiter and Juno and shared Athena's warlike character - as one can see from the statues. She did get Medicine and Poetry and Music added to her attributes though.
Contested Sequel: Naturally, the series as a whole. The most acrimonious sentiment, however, is reserved for The Lost Hero.
Leo in The Lost Hero was shilled as 'the sidekick' and not as important as Piper and Jason. Reviewers described him as the only reason they kept reading.
Nico, too, carrying over from the previous series.
Many felt the Giants were having a tough time filling the shoes of the Titans... Then we met the one good giant, Damasen. He kicks ass.
Even Better Sequel: General consensus has The House of Hades pegged as this, due in no small part to excellent character development, a truly insaneChekhov's Armory pulling from pretty much every corner of the story so far (Think Bob and Calypso), and the journey through Tartarus everyone had been waiting for.
The Reveal that Nico had a crush on Percy in House of Hades has given Percy/Nico quite a popularity boost.
Calypso/Leo has also garnered a lot of fans, thanks to House of Hades.
Foe Yay: Khione is pretty interested in Jason. Jason, on the other hand, not so much.
There's also Leo's even more obvious interest in Khione.
Genius Bonus: Midas' line about an oracle in Omaha was a sly reference to Warren Buffet.
The failed expedition to Alaska was led by a guy named Varus.
Frank is given a spear tipped with a dragon's tooth. In certain myths, whenever a dragon's tooth was planted, it grew a warrior, so anyone familiar with the myths would have caught the purpose of the spear instantly.
Growing the Beard: It's widely agreed that the series really hit its stride in the The Son of Neptune and continued on from there, but special mention has to be made for "the House of Hades", where Character Development comes out in force and the first LGBT character in the Camp Half Blood verse, Nico, is revealed, a step of maturity no one expected to be ever stated outside of Word of God.
Harsher in Hindsight: All the way from the original series. In "The Last Olympian" Annabeth nearly falls off the edge of Olympus, and Percy catches her and manages to pull her up with help from the others. This is very hard to read after the events of "Mark of Athena" where once again, Percy and Annabeth are dangling over an abyss, and no one can help them up. Rather than drop her, Percy lets go and they both fall into the depths of Tartarus!
Also hard to read is back in "The Lightning Thief" when the flying shoes nearly drag Grover down to Tartarus. They realize that the shoes were meant for Percy and share an "I don't want to even think about it" moment when they realize the only thing that saved them was Grover's hooves. Guess they weren't so lucky the second time, huh?
Pretty much all of Nico and Percy's interactions after The Reveal that Nico had a crush on him. It sheds a whole new light on Nico's anger.
Instant Expert: Percy and Annabeth had to go through a significant learning curve spanning several years to become as badass as they are now. The main characters of the Heroes series are able to become just as powerful in less than a week.
Averted with Jason because he's been training at the Roman camp since he was two, and still has his skills even if he doesn't remember how he got them. Ditto with Leo too, kinda, as it seems that Hephestus' kids are gifted with using machines the way Percy's gifted with sailing ships, plus he straight out admits he's a poor fighter and uses his wit or intelligence to get out of most situations. But true for Piper, especially considering her mom's Aphrodite, who's tied with Demeter for second in least warlike of the gods, Hestia being first (in their Greek forms anyway).
It's even still kind of averted in Piper's case too. Almost all of her power comes from charmspeaking, and that's something she's been using for years, albeit without exactly knowing how or why it worked. Her charmspeaking did get more powerful over the course of the book, but it wasn't something she just discovered she had and instantly became an expert in. Played straight with her apparent prowess at wielding daggers, though, such as her slicing up Earthborn with no problem or bringing her dagger to Drew's throat blindingly fast. Even then Piper was still using her charmspeak, specifically she use it to make the Earthborn stand still to allow her to cut the monster up.
In this same vein, Hazel's power over metals and precious gems is something that she worked on for most of her life, ditto for her riding skills, and she trained at the Roman Camp for a year so can fight decently but not up to the level of Percy, Annabeth or Jason. Frank plays this pretty straight though, with his ability to be good at whatever he wants. Though to be fair that relates only to his shapeshifting abilities, his archery is also something he's been practicing for years and he admits he can't fight well with a sword or spear; though he could hold his own, it's not up to the level of Percy or Jason.
Jerkass Woobie: Nico. He's of the Jerk with a Heart of Gold variety and has gone through one heck of a Trauma Conga Line of a life, but it must be said he still is extremely icy and pushes people away rather emphatically, often treating the people who try to understand him with hostility.
Launcher of a Thousand Ships: For being 'the seventh wheel' Leo sure gets around a lot in the fandom. Leo/Piper, Leo/Reyna, Leo/Thalia, Leo/Hazel...And those are only the well known examples.
Magnificent Bitch: Annabeth. What do you do when you have a broken ankle, no backup and no special powers, and nothing to defend yourself but a knife, while trapped miles underground and facing an enormous monster that hates you and everyone you love? Trick it into making a Chinese Handcuff and then trick it into trapping itself inside. Bravo, Annabeth.
If you think about it, it actually makes sense, this time there enemy are beings as powerful as Titan that can only be killed by Gods and Demigods working in tandem, which means that no amount of Mary Sue or Marty Stu is going to cut it without any gods around (and given that most of them are incapacitiated do the Roman-Greek rift that sucks). And there major enemy is the EARTH, not some god who controls the Earth, like Hades. But the EARTH ITSELF, Gaia the literal personification who is literally the Grandmother of all monsters, who masterminded everything in HOO series(and she is ASLEEP while doing this), and is revealed by Aphrodite that if she is awake not only will the Gods can't beat them but she will "shake the western civilization off the earth". The heroes NEED to be Mary Sue in order to survive this type of threat.
Moe: One could argue that Ella at least somewhat fits this trope.
Moral Event Horizon: For many fans, Octavian seemed like a power-hungry jerk who would not do much harm. Then he killed Gwen by stabbing her in the back- and it was just luck that she managed to come back.
Piper's chapters were some of the harder-to-read parts of The Lost Hero, for both her Wangsty inner monologues and being an unfortunate subversion of the typical female treatment in the series. Fortunately, she Takes Several Levels in Badass and becomes considerably more capable and self-assured as the series progresses, to the point where she defeats Zethes, Cal, and freakin' Khione with nothing but her wits, Katoptris, and an awesome application of Charmspeak.
Piper:(to Khione) Still underestimating me. You really need to work on that. *Stab*
On the flip side, Jason was maligned for not enough characterization beyond "Regain my memories, sort out my feelings for Piper, and save the day", being looked down upon as a rather bland Standardized Leader. In The House of Hades, he silenced many of his detractors when he underwent some seriousCharacter Development, became Nico's Secret Keeper, and was forced to make a choice between the Two Roads Before Him.
Ships That Pass In The Night: Leo/Reyna and Leo/Nico are surprisingly popular for pairings involving characters that don't have much overall interaction.
Percy calls home for the first time in months and gets the answering machine.
The later part of Hazel's childhood, particularly her death.
Pretty much everything to do with Nico in House of Hades.
Tough Act to Follow: After the previous series ended in the incredibly high note of The Last Olympian, some of this is to be expected.
They Wasted a Perfectly Good Plot: Embodied in the form of Aeolus, master of the wind. It's explicitly stated that minor gods (Boreas, etc.) are subservient to him. The Aeolian wind spirits mentioned in The Last Olympian are fast and powerful enough to prevent Titans from entering Olympus, at least by air. Everything appears to be setting up for a confrontation with what is arguably the most powerful god that doesn't have a seat on Olympus. When the heroes meet him ... he's a celestial TV weatherman. That's all he does. He tells the weather to a camera that goes to Olympus, and then prepares to do it again in less than a minute. What's more, he has been driven insane by this incredible responsibility that a literal godcouldn't possibly handle, especially since gods can be in more than one place at the same time.
What about the mermaid camp? For everything in Camp Half Blood, there is an aquatic equivalent, with Merpeople being taught by Chiron's aquatic brother, quests, and various heroes, such as Triton and Bill. Perhaps they decided not to do this because Atlantis Is Boring, but it would probably be averted considering the amount of monsters and creatures that are shown to live underwater in the Percy Jackson series.
Unpopular Popular Character: Nico. He creeps out most of the Seven (Hazel being the major exception; he still puts Jason on edge, but Jason is willing to cut him gallons of slack after gaining a better understanding of why he is the way he is) with his whole "son of Hades" thing and generally brooding demeanor. This is not the case with the fandom, where he's well-loved and a main target of fangirls.
The Untwist: The fact that Gaea is the new Big Bad is pretty apparent before you're even halfway through the story as long as you have a decent understanding of Greek Mythology. By the time you reach the point where it is "revealed" to the characters in the story, you kind of feel that Riordan was suffering from a pretty severe case of Cannot Spit It Out.
Values Dissonance: An in-universe example from The Mark of Athena: At Camp Half-Blood, being a child of Athena is nothing out of the ordinary. At Camp Jupiter, however, Minerva is revered as a virgin goddess, so when Annabeth goes there, the Romans are extremely shocked that a child of Athena/Minerva even exists- and that she's leading the quest, since if a child of Minerva did exist, they wouldn't be heading up any quests, they'd be advisers at the most.
Annabeth. She finally got together with Percy, he disappears four months later, and then she finds out he probably doesn't even remember her. He does, but still.
Leo was tricked by Gaea into killing his own mother and then spent the next six or years of his life trying to outrun the pain.
Hazel she was forced by her possessed mother to move to Alaska and raise Alcyoneus, where she made the decision to kill herself and her mother to delay Gaea's plan. Even before she was possessed, Queen Marie was emotionally abusive, blaming Hazel for being cursed. Plus, because of her curse she is indirectly responsible for a number of human deaths which she feels incredibly guilty for.
Frank. His mother was killed fighting overseas, his grandmother died not long after and his whole life is bound to a stick.
Ella. Her treatment at the hands of the other harpies and Phineas is heartwrenching.
At this rate, Percy and Annabeth definitely qualify.
Nico. Freaking. di Angelo. Adding to his baggage from the first series, he escaped Tartarus, and then watched Percy fall with Annabeth into Tartarus. Okay, that's pretty bad, but then it's revealed that Nico is gay/bi and he had a crush on Percy! His reaction to having to admit it to Cupid in front of Jason is heartbreaking, made worse when Jason realizes that Nico was born in the 1930's, when that would have been completely unacceptable. At this rate, the fans are desperate for him to be happy.