The look on Constantine's face when Black Orchid reveals that Zatanna still has feelings for him. It's probably his most vulnerable expression in the entire movie.
Batman's response to Black Orchid's question of how he manages to cope with all the dark aspects of his life ("I have a butler.") is quite heartfelt if you think about it: even after losing his parents, Bruce still had Alfred who continue be the Parental Substitute he needed then and continues now to be the Morality Chain to prevent Batman from possibly one day being consumed by his darker impulses.
All the Ship Tease between Zatanna and Constantine. Though only Zatanna's feelings were revealed, it is clear that they are mutual on Constantine's end. It's even implied that they patch things up at the end of the film.
Constantine and Jason Blood truly getting along after the battle with Faust. It only makes Jason dying and Constantine's clear regret that much sadder.
Etrigan truly caring about Jason Blood, to the point of holding him in his arms when he dies from his wound, along with reciting an eloquent eulogy at his grave. For all the antagonism between man and demon, they had grown on each other after all.
Etrigan: For 500 years, he and I have been bound. A demon from Hell, a knight of renown. Though we were cursed to be slaves to each other, I know of no man I'd want more for a brother. Farewell, mortal.
