Right, how long have you got? 
Cutest:
The scene that my avatar is taken from when he comes back to camp from tending the sheep and yawns then looks up at Ennis with those big blue eyes
or
The smile he gets on his face as Ennis says more words than he's said in a year
or
The excited "little boy at Christmas" act as Ennis makes him meet Alma at the reunion
or
The dimples in his cheeks as he lies in the motel bed with Ennis in his arms and says "Hell, yes I did. Redlined it all the way"
or
The smile when he looks up and sees Ennis arrive at one of their later camping trips
Sexiest:
Unbuckling his belt one handed in the FNIT 
or
The look he gives Ennis as he draws him forward to kiss him in the SNIT 
or
The way he lowers himself onto Ennis in the SNIT 
or
Lying in the motel bed with Ennis 
Well that about covers it for me.
More Cutest: dragging the sheep- cracks me up every time; when he giggles at Ennis harmonica's comment as Ennis sets up the tent.
When Ennis tells him "you'll run them sheep off again...." and he just keeps playing the harmonica and nodding his head.
All of his complaining sessions up on BBM that first summer- I love a complaining Jack.
The shooting the elk scene.
Singing Water Walking Jesus and the way he says "I don't what the pentacost is."
More Sexiest: Even though it is a sad scene, he looks incredibly sexy in the scene where they part ways after coming down from the mountain. The SNIT look (bolded above) is just... no words.
The little "mmmmmm" he gives after Ennis says the sinner line.