Do you have a friend who gets so excited about telling a story that they start explaining each part of it as they tell it and eventually get so off track that they've forgotten what the original story was about? That friend would probably love Eden of the East as this anime ends up losing track of where the hell it is as well.
Story: Ohhhh, so dissapointing. So close to "getting" it only to trip up in the execution. The basis of the story is solid and could easily even be called compelling. 12 random Japanese people are each given a phone credited with 8 billion yen and can grant any wish (for a price) merely by asking it of Juiz, the mysterious female voice on the phone. Each of these 12 "Selecao" has been tasked with saving Japan with their 8 billion yen and is involved in a race to see who can accomplish that goal first. Sounds like a pretty interesting mystery right?
Well after hearing that background, we are treated to an opening scene where the protagonist, Akira Takizawa, wanders up to the White House naked and wielding a handgun (none of this is ever actually explained). So anyways, Akira chose to erase his memories of his days as a Selecao and spends much of the anime trying to discover why it was that he did that. Without spoiling it, I'll just say his reasoning for erasing his memories turns out to be about as illogical as it gets. Outside that dissapointing mystery, there is Akira's determination to discover the purpose/background of this "game" that the Selecao are involved in and his search for the other Selecao.
Honestly the entire plot is boring, unstructured, and completely unfinished. It's a shame to see such a promising premise fall to pieces like this. It's like the writers got halfway through the main mystery of the "game" before going ADD and adding a bunch of other minor mysteries that are rushed and cramped into a few minutes of dialogue before being abandonded as well for the next mystery. The main mystery never gets anywhere close to solved and the audience is just left hanging.
As for a final conclusion, one exists I suppose. It all ends with a final wish from Akira that sounds like something a 5 year old might say. I don't care how much money he has; that final wish isn't coming true. And to do this, he breaks the main rule of the game, but he's apparently allowed to break the rules because, well just because.
Add a container ship filled with thousands of naked, unemployed teenage guys (not kidding), some other Selecao who have motivations that range from bizarre to utterly boring, and impossible wishes taking place immediately, and you have Eden of the East in its entirety.
Animation: It really doesn't get prettier than this. Eden of the East is the most visually appealing anime I've seen to date. Some of the animations when you see a car drive by on the road seem off, but the character designs and backgrounds are fantastic.
Sound: When the story starts in the US, not only do the American characters speak English instead of Japanese (amazing, I know), but they speak English like they are fluent in it. None of the English voice acting sounds like it's coming from a stroke victim a la Chrome Shelled Regios. The music is not exactly catchy, but it's enjoyable. The Japanese voice acting is very good as well.
Characters: The two main characters are Akira and Saki Morimi, the Japanese girl who meets Akira in Washtington DC. Akira is a very engaging character and clearly has depth in the way he's able to appear as a carefree teenage boy for Saki but reveals his maturity when the story progresses into some more serious themes. Saki, conversely, is your typical teenage girl. She doesn't have much character depth and only is involved in the storyline because she has a crush on Akira and follows him around. She does next to nothing to help the plot progress, but she has her own small side stories every now and again and, as these ones are actually completed, I enjoyed them more or less.
There are allied side characters of Akira including some chubby shut-in who hasn't left his room for years since his "trousers" got blown away in the wind... yeah alright. The students in the Eden of the East group are likeable enough though they don't have a major bearing on the story.
The remaining Selecao are all forgettable, confusing, or disturbing. I won't go into details about each Selecao as that's pretty much all you have to look forward to in terms of solutions to your questions. I just want to say one thing about the female Selecao that is introduced towards the end of the series: how much do angel wings cost? She was definitely interesting, though it was the "wtf" type interesting of a two headed lamb or something.
Overall: In sum total, I'd probably actually recommend this anime to people. Eden of the East has likeable main characters and is visually stunning so it's enjoyable to watch. As a mystery series, however, it's a total trainwreck. If you're looking for an anime that is easy to follow and understandable with somewhat linear and complete storylines, this is not the anime that you are looking for. If you're willing to suffer through a number of baffling mysteries with few answers for the sake of an anime with a pretty style, go for it.
Edited 4/21/10 to remove some pseudo-spoilers.