Bittersweet Ending: Everybody moves on to either the next world or to be reincarnated, but the tightly-knit group of friends will be gone forever.
While much of the show could be interpreted as a post-death slice of life high school, the difference here is that nobody gets to see each other again after graduation, unlike other Slice of Life shows. To be sure, everybody finds closure and is able to move on, just as was intended in the world, but the actual memories of the bonds that they shared will be gone, even if/when they meet again in their next lives.
In Otonashi's next life he meets Kanade.
If not the whole Girls Dead Monster band, then at least Iwasawa made it into the music industry. In episode 13 Kanade is listening to and humming "My Song".
Broken Base: Is Yuri cruel or kind? Is Otonashi The Messiah or a fool rushing into things? Is disappearing the best thing that can happen to people in the afterlife?
Complete Monster: The crooks from Yuri's flashback, that threatened to kill to kill her siblings if she doesn't find anything valuable to them. They do and it is implied it was out of impatience or the hell of it.
Crowning Moment of Awesome: All team members that sacrificed themselves in episode 8 got this but TK and Matsushida are the most notable ones. Hinata even lampshades this, by comparing it to a scene from shonen manga.
When Otonashi died in the real world, he gave a particularly awesome showing of keeping a half dozen people alive despite serous injuries and few resources to work with. He tops it by becoming an organ donor, just to able to help a few more people.
Episode 11 has EVERYONE(except Oyama, Fujimaki and Takamatsu) being a badass in the first open battle against the Shadows.
And in episode 12, Yuri destroying the computers that are creating the shadows.
Special Mention goes to the fight with the shadows near the beginning of the episode which included TK spin fighting down a rail shooting shadows, Oyama sniping shadows, and a skinny Matsushita and Otanashi talking while offhandedly shooting and punching the approaching shadows.
Crowning Moment of Heartwarming: Somewhat more depressing than usual, but when Otonashi uses the last of his energy to sign a organ donor card, which makes all the other surving passengers of the train follow his lead.
Hinata explaining how he'd marry Yui at the end of episode 10.
And subsequently the imagined scenes resulting from Hinatas explanation after which Yui disappears.
In episode 12, the source of love that that triggered the doomsday in the afterlife was Yuri all along.
Yuri: I came all this way to protect everyone.
Also in episode 12, the end credits show everybody, even the ones who ascended. It's a nice touch.
Otonashi hugging Naoi at the end of episode 6.
Otonashi: Your life was real too!
It was heartwarming when Otonashi recalls his death and wonders what became of his donated organs and Kanade reassures him that the person receiving them would thank him for the rest of their lives. But it becomes a true crowning moment in hindsight when you realise Kanade wasn't just guessing.
For being named after a guy who's name means 'No Sound', Otonashi is quite the earful.
Deus Ex Machina: In episode 12 there's Yuri's vision (which she receives out of nowhere) of her brothers and sisters telling her she's done enough and it's okay to end her war with God. She listens and ends her war.
Downer Ending: It seemed like a bitter-sweet ending at first with everyone saying good-bye and disappearing but moving on with something better. Then after Otonashi confesses his love for Kanade, asking to stay with him forever, Kanade reveals that she's only here to thank him for the heart transplant that saved her life for a while, and disappears after Otonashi had to say he loves her again. Otonashi is left all alone and heartbroken for the last of his time before he disappears.
It certainly felt more so if you see the epilogue not as an afterlife or reincarnation, but rather Otonashi's own imagining or false memory of meeting Kanade again to help him move on. But,again, an alternative ending has been confirmed.
It's implied that Otonashi also disappears and finds Kanade in his next life, making this quite a happy ending viewed that way.
YMMV depending on what your interpret that epilogue to be exactly; see above.
And even if you interpret the ending straightly, there's still the fact that it feels like an Ass Pull just because the creators thought the real ending was too sad; or worse, the result of more Executive Meddling.
Dude, Not Funny: Yes, pulling all of those stunts to make Angel fail her tests was hilarious. However, it suddenly stops being so amusing when you realize that: a) Angel is a real human girl named Kanade Tachibana and had to suffer the consequences for getting zeroes on all her tests and b) Naoi, her Ax Crazy vice-president, replaced her. Oh, and just to rub the salt into the wound a bit more they then go and steal her comfort food. Seriously, she's so sad, it makes you want to give her a hug.
For this troper, it was the moment that Tenshi moved from 'that kind of cute girl they keep fighting who probably isn't as bad as they think' to 'oh my word this is probably going to be my favourite character in this show' (a prediction borne out following future episodes). It was also something of a Growing the Beard moment for the show in general for this troper; before that, it had been a very good show, but at that moment it became excellent.
On this very wiki, Naoi's section is huge compared to other character's
Epileptic Trees: There've been a few here and there, but it wasn't until the appearance of the red-eyed Angel that they started spreading like wildfire.
Anonymous: I see what's going on. You are really TK, who is God, but Yurippe beats you and takes you memories, and then she becomes God, but she knew Otonashi in her past life, who was her childhood friend, but she fell in love with him, and when as God she realized he was going to die, so she made his sister who is really Angel who is waiting for Otonashi into the enemy and with her God powers made this world so that when Otonashi got there he would think Angel was the enemy and now she made a new Angel after Otonashi befriended the old one who is really his sister and she wants to tear them apart.
There's also Red Angel and Gold Angel, based on their eye colors, to differentiate between the two.
The SSS Brigade!
Funny Aneurysm Moment: Yui prevents Hinata from winning his team's baseball game in episode 4. Six episodes later, Hinata helps her move on by promising to marry her in her next life even if she's paralyzed in that life too, meaning if it weren't for him she'd be stuck in Purgatory for a long time!
Genre Savvy: EVERYONE. To the extent that can be called dangerous. Some battles are won or lost depending on who is more genre savvy. This even affects the plot: the movie is an action anime, until everyone realizes that they star in a drama.
Glurge: The Aesop seemed to be: "Any desires you may have or actions you may take are completely useless and you shouldn't have them. Strive instead for nonexistence. All you should want is to be erased, you and your meaningless journey though life."
Hand Wave: The anime just handwaved the reason of Takamatsu's sudden change from an NPC back to 'human' and his disappearance.
Not entirely, as Yuri also broke free of being an NPC in the previous episode, so it had already been shown that it could be done.
Moral Event Horizon: Averted in the manga. In order to force God out of hiding, Yuri seriously considers killing every single student in the entire school... Starting with the first graders. Thankfully, Hinata talks her out of it.
Also averted in Stairway to Heaven due to a Foregone Conclusion from watching the entire anime. Yuri makes everyone starve over a simple miscalculation she had made; however, the anime had already established her as redeemable by the time Stairway to Heaven rolled along.
Never Trust a Trailer: The next episode previews just consist of a white screen with random lines from the next episode flying by. The lines are quite out of context so deducting any clues about the plot of the next episode from this is next to impossible.
On top of that, every Monday the online preview adds short, half-second clips from the next episode. This can answer some questions, but often raises many more.
They Wasted a Perfectly Good Plot: Since the anime is only 13 episodes long, there isn't a lot of time to focus on any of the interesting side characters, so they come and go without us knowing anything about their pasts, nor do they get a decent sendoff onscreen.
What an Idiot!: Even after all the time they've been fighting Angel, nobody in SSS has ever bothered trying to figure out Angel's real name.
Well, Yuri had apparently heard it before. She just didn't bother trying to remember it.
Also, in episode 8, Yuri attempts to reprogram Angel's Harmonics technique, but has trouble because she doesn't quite understand the programming language. Remember that SSS has Christ Takeyama, who is a master hacker and computer expert, and he doesn't even show up in the episode at all! Although Takeyama became A Twinkle in the Sky in the last episode, he was seen again during the fish barbeque, so his absence from episode 8 is even more jarring.
Most of the cast also qualify but varies from character to character. Yuri, Masami, Naoi and Yui have significantly worse pasts consisting of murder of loved ones, guilt and death, parental abuse and death, death of loved ones and long term paralysis respectively than say Hinata whose only regret was not being able to catch a baseball costing his team an important match. That's it. Other characters don't even have that much development.