Satsuki
& Yuuto ( with BEAST watching jealously in the background)
This is a big one. Satsuki and Yuuto are continuously seen together. While she searches for information or goes to battle Yuuto always seems to arrive there when she's finished so that he can either look concerned or take her for tea. There's no clear declaration that these two are a couple, but there's definetily something going on.
Satsuki views humans as boring, but Yuuto's company is still welcome and enjoyable to her. Yuuto is something of a playboy, yet he spends time with a girl who isn't his usual type, being very intellectual and reserved. It is more than just friendliness to a fellow Angel, because we've seen that the Angels aren't that big on teamwork and loving relationships.
It is safe to say that Yuuto is one of the few humans, perhaps the only one, whose company Satsuki accepts. She doesn't neglect him in favor of a computer. And Yuuto? He sees something in her that his previous companions haven't had. A challenge, to make her feel; a change, to be with someone so different; a partner who understands what the End of the World means.
Satsuki & Kanoe
What is going on here? In the early volumes where Satsuki spends her time gathering information in the basement Kanoe seems to be rather constantly getting close to her. You could say that the Dreamgazer is trying to be patronizing, but that doesn't fit if you take in the fact that Satsuki's an adult and very, very capable of rational thought ( she's smarter than Kanoe). Or it might just be Kanoe's habit of getting physical with everyone. Ah, well.
Satsuki & Yuzuriha
She killed Yuzu's beloved inugami, who had been her companion since childhood. Even the genki and cheerful Seal wouldn't forgive something like that. I'm betting that Yuzuriha would really want to see Satsuki get punished for that. Perhaps killing BEAST, one pet for another. But CLAMP will probably never go there, so it's just and idea in Miko Keiishi's head.
Satsuki & Arashi
She hurt Sorata. Arashi will want to make her pay.
Satsuki & Sorata
See above. Sorata won't think very fondly
of the person who almost made him die for Arashi before he'd actually gotten
anywhere with her.