Regarding June's quote about the amount of men she's dated, it was most likely intentional considering how many other hints and plays on root numbers they hid in the game. (Cap's bracelet, the coffin combination, etc.)Just got this game a few days ago for my birthday, and recently got the last ending I needed (Axe).
A couple things I didn't see mentioned here or on the answers page on the official site (sorry if they were though):
Does anybody else think the game foreshadowed June's true identity and bracelet number pretty early on? At one point she tells Junpei the number of men she's dated is, "18... times 0."
1 + 8 = 9 (her bracelet number)
18 x 0 = 0 (she's Zero)
I also saw people wondering why she got a fever after the 9th man was killed, and unless I'm remembering wrong, they didn't answer this on the official site. So was that fever caused because their version of the Nonary Game was already different than the one held nine years ago due to the death of the 9th man? And I'm assuming the fever went away as the game got back on track since having the 9th man out of the game wouldn't hinder the progress of the rest of the participants.
Regarding her fever when the 9th man dies, I remember having some discussions about that before. As you mentioned, the common assumption is that June's fever is a direct result of something happening during the nonary game that doesn't lead to Junpei reaching the final puzzle, but her first fever attack in the game is unavoidable. This leads to speculation that the 9th Man wasn't supposed to die, or at least not at that time, but she was still able to course correct despite that occurance.
My question is then, is there a "perfect" run through of the nonary game? One where she never has a fever? (And if so, why isn't it available in the game?) Or is this just the route that has the least amount of variables that can get things off course? Meaning, the death of the 9th Man is a branching point that can ultimately lead to multiple different scenarios that could result in June disappearing, in addition to possibility of the desired outcome of Junepei reaching the end.
It would of been cool IMO if after you unlock the Safe ending you could play through the game without the 9th Man dying. (Perhaps you'd still hear the explosion, but when the door opens, his body isn't there and he pops up later, after you go through door #9.) Of course, they'd have to change some other plot points, so it may have been too much to ask. Still an interesting idea though.