The Garden of Sinners/WMG

SHIKI knew about the 3rd personality

 * SHIKI (the male personality) may have had a greater connection to Akasha than Shiki did at the time. Shiki may possibly have caught wind of the fact that the Counter Force was manipulating events in the long run to get Shiki to eliminate Araya. SHIKI then realized that he would have to die in order for the 3rd personality to manifest, spurring him to try to kill Araya on the road after chasing Kokutou. Realizing he couldn't, he then attempted suicide, knowing Shiki would survive and he would not. This explains the one shot in Paradox Spiral, where Shiki or SHIKI glances at the "camera" in the flashback. (This theory does not take information from the novels into account).
 * It's implied in Paradox Spiral that Araya influenced Tomoe. The glance at the camera is a teaser/ContinuityNod to the epilogue since it's mentioned by Touko that the dream that Shiki is having is the entire history of the world.

Azaka is bisexual
Less of a WMG and more of a heavy implication, given her Origin. Her incestuous feelings simply push this (and who knows what else) further in the background. Also...

Azaka and Seo Shizune will have a relationship
The vision Seo had when meeting Azaka at the end of Mirai Fukuin isn't just of their friendship, but of a future relationship. As soon as Azaka gets over losing her brother to Shiki, her friendship with Shizune will grow to be much more.

...and Azaka will end up being jealous of her own brother when she falls for Shiki
Because it's obvious the poor girl can't get a break. Expect the Harem Solution to be among her proposals...

Mikiya saw her whole relationship with Shiki and even her daughter, if not most of the events of the series
Mirai Fukuin reveals that Mikiya does have minor powers of clairvoyance. He can see an hour or a day in the future. However, while Seo Shizune finds herself burdened by this power, Mikiya reveals how he dealt with it: by pushing his power further rather than trying to suppress them. The Distant Finale and very last portion of Mirai Fukuin is called a Preface precisely because it's the first serious prophecy Mikiya saw while experimenting with his powers, well before even meeting Shiki.

Touko has Mystic Eyes of Appearing to Be Extremely Rude
She treats them like split personalities, which plays even more to the series' theme (Mikya/Azaka, Shiki/Shiki), but the reason she appears to be much more rude without her eyeglasses is because of the influence of her Mystic Eyes. She's actually the same both ways. This might also be the reason why Cornelius Alba gets so pissed at Touko: he's under the influence of her Eyes, and finds her to be much more rude than she actually is.
 * Which brings us to a nice moment of Fridge Logic: how did Aoko get Touko to make her eyeglasses for Shiki Tohno, when the sisters aren't exactly on speaking terms? She didn't; she just stole a pair of Touko's Mystic Eye-blocking glasses when she had put them down somewhere.
 * As for her multiple bodies, remember that the Mystic Eyes aren't part of the actual eyes, but are part of the soul and Origin; Shiki would eventually see the lines of death even without her physical eyes.
 * It's possible that her multiple bodies are precisely the reason Touko knows this.

Some of Touko's dolls have physical differences.
Hence her changing appearances across media.