Angst? What Angst?: The preteen to teenage main characters aren't nearly as psychologically affected by always having to fight monsters that are trying to kill them so often as they probably would be in real life. At the very least, there's no sign of PTSD. However, given that they have to do this for years on end, it could be safe to assume they just get desensitized by it, or as demigods are more geared to handle such things.
Anti-Climax Boss: Every big threat in The Last Olympian. The Drakon dies in six pages, and Kronos barely fights enough to look strong. Even in the last fight it didn't take too long to bring him down. Even Typhon.
Especially Typhon. At least the others had actual battle scenes where the hero had to struggle. It might be justified, however, since he's described battling the whole pantheon during the final battle, but even so we see very little of that.
Crack Pairing: Tons. Rachel/Nico, Thalia/Nico, Percy/Clarisse, Rachel/Luke, Apollo/Hermesnote Which is actually technically possible in the source material, especially given the fact that both are involved in same-sex relationships with mortals and other gods, etc.
Ensemble Darkhorse: Nico di Angelo gets the most love in this category, going from cute, annoying kid to an emo badass over the course of the series.
Fandom still showers attention on his sister, Bianca di Angelo, too. Never mind that she dies in her introductory book. Many fanfics explore either her life after death or her life in a "What if?" scenario should she have lived.
The twins, Artemis and Apollo, also get a lot of love, despite their very minor appearances. Quite a few fanfics are dedicated to them.
Similar to the above, the Hunters of Artemis get a lot of attention in fanfic, especially notable considering that very few members are named. Artemis's lieutenant, Zoë Nightshade, is especially popular.
Calypso has quite the following, and avoids the Die for Our Ship treatment that Rachel first suffered. Many rejoiced when she returned in the sequel series.
Even Better Sequel: Most agree that the books get better with each installment. The Battle of The Labyrinth had even more of awesome moments and Character Development in comparison to the already strong Titan's Curse.
The Last Olympian, big time.
Fan-Preferred Couple: While Percy/Annabeth is still dominant, there are still rather decently sized fandoms for Percy/Luke, Percy/Nico, Percy/Artemis, Apollo/Hermes, Poseidon/Athena and Percy/Thalia.
Foe Romance Subtext: Luke and pretty much everyone. Particularly Percy, Thalia, Annabeth, and (if you squint) Grover.
"Funny Aneurysm" Moment: Percy and Nico's first meeting is a pretty funny scene where Percy saves Nico's life and Nico proceeds to talk his ear off about mythology. It's significantly harsher after The Heroes of Olympus showed a glimpse of Nico's POV in that scene—basically, he saw Percy as a mythical hero come to life, which only made his crush and Percy's failure to save Bianca that much harder for him to accept.
If you live in Washington, D.C., you may have figured out the plot twist about Bianca and Nico di Angelo in The Titan's Curse prior to the reveal that they spent time in the Lotus Hotel & Casino: To evade their pursuers in Washington, D.C., they duck into the Washington Metro. Bianca says the Metro is new to her, and she even mentions that the last time she and Nico came through D.C. (which was no less than a year prior to the events of the story), the Washington Metro did not exist. Just for the record: the story is set in 2007. The di Angelo siblings are in their early teens. It seems odd that Bianca would make such a remark when the first segments of the Washington Metro system opened in 1976, well before either Nico or Bianca would have been born. Once Percy deduces that they spent time in the Lotus Hotel & Casino, it makes sense that they must have entered it sometime before construction of the Washington Metro ever started. The Last Olympian reveals that they were actually born sometime in the mid-1930s, and put in the Lotus Hotel sometime around 1941.
It might or might not be intentional, but the mention of a statue of Susan B. Anthony strangling Frederick Douglass in The Last Olympian might be a roundabout reference to how the two civil rights leaders, formerly steadfast allies, became divided over the issue of the Fourteenth Amendment allowing black males to vote, but not women of any race (and to add insult to injury, it was the first Amendment that explicitly mentioned male and only male citizens).
Growing the Beard: Most agree that The Titan's Curse was where the series really began to show its quality.
Harsher in Hindsight: Percy catching Annabeth when she nearly falls off Olympus becomes cringe worthy after the events of the third The Heroes of Olympus book, Mark of Athena, where he catches her again while she's being dragged by Arachne's threads into Tartarus and this time around, he chooses to fall with her.
Promise (which seems to be the Arc Words in Luke's life), after reading The Diary of Luke Castellan.
The tense relationship between Nico and Percy becomes downright depressing after House of Hades, where it's revealed he was hiding his true feelings from him.
Inferred Holocaust: In the first book when Percy, Annabeth, and Grover face Hades, the god of the dead becomes so enraged that he causes not one but two earthquakes, and Percy remarks that it will not have been a peaceful night in L.A. When the kids resurface, Los Angeles is burning. No casualty numbers are given, but it could qualify as a "Funny Aneurysm" Moment, as Hades had just finished complaining about how the Underworld was overcrowded and didn't need more subjects. Kinda ironic.
Manhattan sounds pretty bad by the end of the last book. Everyone had fallen asleep, which probably includes people who were cooking things, people who were in the hospital getting surgery, etc. And Fifth Avenue is a disaster.
I Knew It: Who is the lightning thief? Could it possibly be Luke, the swordsman who is a son of the god of thieves, and has a scar running across his face?
Les Yay: Silena and Clarisse, Annabeth and Thalia, Zoë and Bianca.
Zoë and Artemis, one-sided on Zoë's part, arguably.
Clarisse and Silena in particularly considering they play out the relationship between Achilles and Patroclus to its tragic conclusion. And we all know about them.
Rewatch Bonus: For those that read the sequel series, every single scene regarding Nico and Percy takes on new meaning once you learn Nico had a crush on Percy since the day he was rescued.
The Untwist: The fulfilling of the prophecy in The Titan's Curse It says "One will be lost" and everybody assumes it means someone will die. But it never outright states dying, so with the usual Prophecy Twist you could expect Bianca to be lost and later found. It turns out she gets Killed Off for Real.
The Woobie: Everyone not named Gabe, Ares, or Kronos.
Luke's mother, May Castellan, also deserves a special mention here.
In The Last Olympian, the narration actually says that Hermes "looked like he needed a hug." If that's not baiting woobiedom, nothing is.
MRS. JACKSON. Ridiculously nice, sweet, and caring, and yet gets get stuck with an abusive slob of a husband and serious financial problems. Luckily, things get much better.
Even Dionysus has a little of this after he revealed his relationship with Ariadne to Percy in the third book, and after one of his sons dies in the fourth book.
Tropes which only apply to the film:
Angst? What Angst?: Percy seems to handle the sudden death / disappearance of his mother very well...
Anti-Climax Boss: Kronos in Sea of Monsters, possibly intentional because the rest of the books might not be adapted to film.
Broken Base: Whether or not Annabeth counts as a Faux Action Girl. Those who claim she is point to the fact that she has to be saved from Medusa by Percy, doesn't figure out the Lotus hallucination until after they're outside it and then does nothing in the climax - despite claiming to have lots of experience with battle strategy at camp. Those who say she isn't point to her beating Percy in their first duel (and he needs a power boost from water to match her), being the one to use Car Fu against Medusa, successfully shooting some guards and the hydra and merely being Overshadowed by Awesome - since only one person can wear Hermes's sneakers. Rule of Cautious Editing Judgement really applies here.
Evil Is Sexy: Medusa. Of course, she is played by Uma Thurman.
Both films. Some fans detest them due to how different they are from the book, others regard them as bad adaptations but decent enough films.
The Sea of Monsters film. Some thought the movie was worse than the first, others thought it was better and more entertaining.
Nightmare Fuel: The scene in Medusa's shop. While it isn't that creepy in the book (there the scene is a lot less ominous up until the Uncle Ferdinand bit), the movie added a panicking woman whose husband had already been turned to stone and she's hysterical with fright. She eventually gets turned into stone too, and the only mention that's made of it is when Annabeth explains how she scraped her wrist (the woman had been holding her wrist when she had been turned to stone and Annabeth had to pull her hand free).