What makes it Heartwarming is that Edward refuses to hold her because he knows he might hurt her but Kim wordlessly (and carefully) wraps his arms around her and hold them to her chest as they both close their eyes. Lost in one moment of tranquility in possibly the worst night of both their lives.
The fact that Edward committed a robbery, irreversibly damaging his reputation in the process, for the simplest reason:
Edward: I knew it was Jim's house.
Kim: You...you did?
Kim: ...Well, then... why'd you do it?
Edward: Because you asked me to.
Despite her bad treatment of him in the beginning, and knowing that they were asking him to break the law, he still did it just because the woman he loved asked him to do it...
One guest at Peg's barbeque telling Edward not to let people treat him like an invalid.
Which becomes Harsher in Hindsight as he later calls Edward a cripple when the whole town has turned against him.
Edward lovingly dusting off the lawn chair for Peg when he prepares to cut her hair- she's the closest thing to a mother he's ever had, and that little moment shows how much he cares for her.
The loving smile she gives him before he cuts her hair gets me every time.
Vincent Price's performance in general, doubling as a massive tear jerker. It was his last role, and the effects of his age were clearly creeping up on him, but nevertheless, he very obviously gave it his all.
While a Tear Jerker as The Inventor died before he could give Edward his hands, there is something about his smile as Edward looks at the hands that touches the heart. You can tell Vincent was proud of doing this role when he was alive.