Makoto cheats death, goes back in time and becomes the original Sawatari Makoto.Mishio clearly states that the sacrifice that Makoto must give To Become Human is comprised of two parts: her memory and her life. However, Ayu creates a much, much stronger miracle, only loses a small fraction of her memory (whereas Makoto forgot her entire history), and lives to tell about it, even surviving a Really Dead Montage. So could it be that when we saw Makoto laying on a green, sunny Monomi Hill, it wasn't Yuuichi thinking about how he would revive her, but she really was back... somewhere? We know that Ayu's super-miracle fixed up the other girls' lives overnight, even when they seemed completely helpless. There's no reason to believe that she wouldn't be able to send Makoto back in time and return her to human form. There, knowing human customs and the history, she would be able to replace the original Sawatari Makoto (who may have died shortly after birth?) and live through that life. The 2006 version of the show plays with the idea; the real Sawatari Makoto is shown to look and sound like an older version of the one we know, with the same love of meat buns and bells, which is clearly stated to come from her fox side. Also, in the very end, a fox appears that looks just like Makoto's fox form. (Great, now I'm going to start believing this.)
The entire series is Ayu's dream, up to the last few moments.At the beginning of the third episode, Ayu's 'dream' monologue mentions, "How long has it been since I realized this was a dream? A few minutes, or much longer?" or something to that effect. In the immediately previous episode, when complaining about Yuuichi dodging her, she makes a point about emphasizing the "ruined drama". Ordinarily this would be just your run of the mill Fourth Wall busting, but think about it: all the fantastic things that happen to Yuuichi that can't happen in the real world, where the series is set, make perfect sense in the context of a dream. And the town is small enough that it would be unreasonable to think that all these girls (or animals or what have you) connected to Yuuichi would be completely unaware of each other's existence. This also answers why Akiko doesn't reveal the critical detail of Ayu's existence: in the "real" real world, she does. Almost immediately, in fact; subsequently, Yuuichi goes to the hospital to an awakening Ayu. The dream, therefore, is in the last few minutes of her coma, within a few days of Yuuichi coming to town.
Most of the series is real, but the last few scenes (after Yuuichi finds the headband) are a dream.The opposite of the WMG above, in other words. Ayu's supernatural dream lets her meet Yuuichi in the real world and heal several of his friends, but this dream fades out around the time Ayu vanishes (her background narration says the dream is ending at about this time). A somewhat depressing take on things, but it does explain a few oddities; mainly the blurred dreamlike appearance of much of the last few scenes, and the fact that Ayu could project a copy of herself into the physical world and magically heal a bunch of people, yet couldn't heal herself and seemingly thought Mai couldn't help her either (why would Ayu get better long after the people she healed, instead of at the same time? Invoked Rule of Drama?). The headband-giving scene could only be a dream of Yuuichi's (unless Time Travel is involved), which makes the following and final scene, with Ayu awake for no stated reason, all the more suspicious. She probably does wake up eventually—kinda hard for Yuuichi to "always be smiling" if his girlfriend's in a coma—but the way it's shown in the end seems ambiguous on purpose.
The reason that Akiko is so accepting of the Pretty Freeloaders is that she's was in Yuuichi's position when she was youngerAt least one other person (Mishio Amane) has had similar experiences to Yuuichi so there's no reason that it couldn't have happened to others. Akiko just happens to be one of them. It logically follows that...
Nayuki's father is some sort of supernatural entityWe never see him because he's passed on, vanished, no longer able to take human form something.
"That Jam" is JarateYellow? Check. In a jar? Check. Adverse effects on anyone who comes in contact with it? Check.
Yuichi is KyonThis is probably what would've happened had Kyon of gone to a school other than North High. And then ran into a bunch of girls who had issues. I know, same voice actor, but his dialogue/sarcasm mode seems to fit both characters.
Freddy Krueger was involved.Freddy was responsible for Ayu dreams but Jason Voorhees killed him before he could do any thing.
Mr. Minase was a fox.We know that Akiko already knows about ikiryou from how she automatically understands Ayu's situation, but as CLANNAD proved, under normal circumstances (without a miracle like Ayu's), ikiryou are forgotten once discovered and proven (poor Fuuko), so he couldn't have been one of those. But Mai knew about ikiryou too, from her experience with other supernatural phenomena. Akiko is also unbelievably accepting of Makoto and understanding of her situation, doesn't question the ending of her route, and in the 2006 anime, breaks down crying after Yuuichi and Makoto leave the house for the last time, implying that she knows Makoto won't be coming back. We also know that there was at least one fox spirit before Makoto (see Mishio) and that there are likely to have been more (as Nayuki mentions that it's a legend around town). So, Nayuki's father was a fox, and he isn't around because he disappeared after sacrificing memory and life.
Mai was the demons.She's been having severe psychological issues as a result of her very sad backstory. Any harm she did to herself or others was actually her own doing. The pressure and stress of dancing in front of a crowd of people who were whispering to each other about her being a "troublemaker" caused her to have a nervous breakdown in the dance scene - there were no demons, she was just destroying the room.