The first indicator that Kat is warming to Patrick - although it involves him embarrassing himself at a club. While she does laugh at it, she gives him a soft smile, indicating she liked the compliment all the same. She also cutely teases him as he asks her to the party.
Patrick looking out and taking care of Kat all throughout the party, even after Cameron tells him the deal is off.
Patrick genuinely telling Cameron that Joey isn't half the man he is and that he should go after Bianca.
Speaking of Bogey's party, Bianca starting to realize that Joey is completely vapid and so slightly starting to fall for Cameron, while Patrick spends the entire night keeping Kat safe.
Patrick singing to Kat on the soccer field.
And Kat returning the favor by flashing the teacher to help him to escape the ensuing detention.
While a somewhat sad moment, Kat looking down out her window at Bianca, devastated that she can't go to the prom and knowing it's all her own fault, then the following scene where she is seen walking out the door to go to the prom, beginning the segue into a Moment of Funny.
And then there's Cameron, Bianca, Kat, Patrick, Mandella, and Michael meeting up at the prom. Michael dresses up as Shakespeare and gives Mandella a period dress, because he knows how much she loves Shakespeare. Cameron and Bianca get snuggly and are laughing together. Kat squees over her favorite band playing (which Patrick arranged to have happen, even though he hates their music). There's a moment where Bianca and Kat smile at each other, which is the friendliest they've been together throughout the movie. It's just so sweet overall!
The day after the prom, when Bianca sincerely thanks Kat for going so that she could go, and telling her how good a time she had, to which Kat responds, "I'm glad." Despite how awful the night turned out for her, she's honestly happy for Bianca. And Bianca shows again how much she's grown when Cameron comes by to take Bianca out, and as they're leaving, they turn to look at Kat:
Cameron: Is she going to be okay? Bianca: I hope so.
Kat and her dad having a heart-to-heart as well as letting her go off to college on the other side of the country. Then, when it's revealed Mr Stratford sent Sarah Lawrence a check so Kat can attend, it becomes very sweet when Kat hugs him, considering their animosity earlier in the film.
