Dunno if already mentioned, but Kate's new quest "A Single Moment" requires you to have three moments of glory. Here they are:
1. Resolve, in Twisted Fate: when Kate asks you if you're perving on the cheerleaders again, say that you were leaving.
2. Strength, in Twisted Fate: must have 8 STR. Fight the cheerleaders.
3. Insight, in Wicked Game: dress as a ghost, instead of getting inside the box. When Kate asks her sins, answer "your fears..."
4. Talent, in Dead Girl's Score: as Lindsey praises you for playing the piano, play something fast but dark. Suddenly Kate "u suck lol lmao". Tell her to show how it's done.
5. Wit, in Twisted Desire: must have 9 INT. When Kate asks to see the golden star, let her snatch it... then call Isabelle as a witness that you did get the star.
Moments #1 and #2 are mutually exclusive.
I've heard that A Single Moment is actually necessary to pursue Kate later on, but I'm not so sure.