Yes, yes they do.
Now that I've caught your attention...

Look at me. I'm gone for a couple of days and I miss the day the video for The Son of Neptune came out. I hate fate. I mean, fate, not the Fates... They're the same thing, aren't they...?

Anyways... This is my analysis for that video that LeoV44 posted (many thanks, here's a banana), we now A LOT more information than we had a few months ago, even though that video was only like a minute.

I'd post the video in this article if I could. Unfortunately, I can't, since I don't have a computer with me right now. But I can post the link. link, but the video is already posted in the Videos section, so you can go there instead anyway.
I'd also post pictures in this article if I could, but I can't because I'm typing every single thing you read here from an iPad. I hope you appreciate all the work I'm doing!

To most people, the things that will probably stand out in the video are the character art. Not me (yep, I'm weird that way). For some reason, the one thing that stood out to me is the part about the Doors of Death.
You see, Rick Riordan (known to us as RR) said that the heroes will have to travel to Greece and find the Doors of Death. When he said that, I was like, "What?"
Because of this one simple fact, we can hypothesize (fancy science-y word, thank you very much) that the Doors of Death is not the one in DOA Recording Studios in LA, or the one in Central Park made by Orpheus. Also, we now know that the quest-keteers will have to find the Doors if Death, not just stumble across it by accident. If it were to happen like that, I'd bet big money that Leo is gonna be the one who finds it by accident... So, what place in Ancient Greek mythology would the Doors of Death be? I have no idea. You'd have to ask RR himself, and he's not gonna give it up easily.
That's what theories are for!

1) It could be inside the Labyrinth. You go through the maze and find the literal Door(s) of Death. But the problem is, the Labyrinth was destroyed in The Battle of the Labyrinth when Daedalus died. So it can't be this... But it was a good idea, right?

2) It could be in the Sea of Monsters. Somehow I doubt this. RR wouldn't use the same place as a center of adventure twice (I hope). The Sea of Monsters is familiar to us, and the point of reading is to explore whole new worlds. In the Percy Jackson and the Olympians series, we get introduced to a new place each book. So it's unlikely the Doors of Death is going to be here.

3) Crete. I don't know, a gut feeling...

4) Hades is the one they're gonna ask. Being the god of Death, it makes sense if he knows every door-of-death-like entrance. So maybe it'll go something like this:

"Dad?" Hazel asked.
"What?" Pluto growled. Hazel looked at her friends for support.
Jason stepped up. "Lord Pluto... Uncle... Do you know where the Doors of Death is?"
Pluto leaned back on his throne. "Why, yes, yes I do. It is in-You there! Do not touch that!"
Frank jumped back, pulling his hand away from a vase with swirls of darkness moving inside.
Pluto turned back to Jason. "As I was saying, before that wretched son of Mars interrupted me -"
"I am not wretched!"
"-the Doors of Death is in [insert where the Doors of Death is here]"
Hazel smiled. "Thanks, Daddy."
Pluto had a glint is his eye. "Yes... Now as for the payment..."
"What?" Leo was looked at Pluto. "Payment? You didn't say there was gonna be a payment!"
"You didn't ask." Pluto continued, "I want all seven of you to..."

Yeah... Something like that...

5) The Doors of Death is just part of RR's imagination and he's gonna put it in a completely random place where the quest-keteers will eventually be.

Another thing about the Doors of Death: It's plural.
Does that mean that they're gonna have to find several Doors? Or that there's several doors in one place and they're gonna have to pick which one is the real one or else they die? Or maybe it's just a big double-door. Either or, we'll find out when the booms comes out...

Now, it's time for Character Predictions! (Because we all love Character Predictions and it makes us feel good that we know/guess a lot of information from such few clues.)

1) Bow and Arrow Guy (from here on, he's Bag):
Yes, we all see the bow and arrow he's holding (you'd have to be blind to not see it). That alone makes it a strong possibility that he's a son of Apollo. But, just because he's holding a bow, doesn't mean he's a son of Apollo. Look at Annabeth, she knows how to use a bow, but she's not a child of Apollo. And Chiron. Bag looks more like a son of Mars to me... In fact, I'll clearly state my opinion right now: HE IS A SON OF MARS. Mars is the god of war, right? So it would make sense that he knows weapons (Ares said it in The Lightning Thief, I think). So maybe this son of Mars just picked a bow and arrow as his weapon of choice. And look at the shadow! (Now I really wish I can put a picture in here) Looks kind of like a bear, right? But the bear is Artemis's animal. So, second guess: looks kind of like a dog. A dog is a sign of Mars (a sign of Ares actually, but I'm gonna assume it's the same for both).
So yes, I do think he's a son of Mars.

2) Teddy Bear Dude (from here on, he's Teddy):
He is holding a bear. And he us wearing a toga. And the background looms like fluffily clouds. And his eyes looked ready to drop, like he's going to fall asleep any moment. What does this mean? I smell a strong possibility for a child of Somnus. Well, I have no idea why he's wearing a toga, but that's his problem, not mine. Is there a god/goddess of togas? Who invented togas? The mysteries of the universe... Anyway, yeah I think he's a son of Somnus. *Snickers* Sorry, but why is he holding a teddy bear? Why does he even have a Teddy bear? And look! There's like a green stuffed bunny behind him! Unless he is less than 10 years old (he could be... It's hard to tell his age...), him having a Teddy bear us kind of... Weird. I mean no offense to Annabeth. *dodges knife* I SAID NO OFFENCE! So yeah, there's also a possibility that Teddy is 10 years old, or younger. If so, he looks old for a 10 year old. But he can also be a son of Apollo or Minerva. He is blond. Maybe he's a son of Apollo/Minderva who has an attachment to his stuffed animals from his childhood. If he is a son of Somnus, then he won't be part of the prophecy. If he is a son of Apollo or Minerva, then he might be a part of the prophecy. I think the latter is a better possibility. The artist wouldn't draw a picture of a minor character... Unless he's a major character but working outside the prophecy! Yeah... Sure, let's go with that...

3) Lady with Dogs (from here on, she's Lady Dog):
I think she's a goddess. What kind of demigod would wear that toga and keep a pet dog? ... Fine, there might be a demigod weird enough to do that (mostly the toga part, having a dog is perfectly normal), but still! She's sitting on a throne! Isn't that clue enough? If there's a goddess of dogs out there, I'd be interested to know.

4) Lady Riding a Horse (from here on, she's Horse Woman):
Might she be Hazel? I can't get a clear look at her eyes. If her eyes are hazel... Anyway, I'm not here to figure out their names, just their parentage... She's riding a horse, so is she a daughter of Neptune? If she is, then she might be part of the prophecy... But no, Percy is already an almost-positive for the seven. You can't have two of the same parentage. Percy is one of the seven because RR freaking dedicated 1/3 of a book in HoO for him! So yeah... But other than that, I have no idea who Horse Woman is... Yes, woman. I think she looks more like a woman than a girl. Could she be a goddess?

Ok, that's all... For now. My fingers are hurting. I might post some more of my opinions in the comments though.
So, I'd like to hear what you think of the things above. Whether I'm illogical, stupid, genius, crazy, whatever.

I'd put a picture of a monkey eating a banana, but, like I said, I'm using an iPad.