The line "Peter, I worried about you so!" just piles on the emotion. Here Shadow is limping and having gone through an incredible ordeal and he says he was worried (although Peter was worried about Shadow too.)
Shadow's speech about why dogs attach themselves to humans:
Shadow: ...I shouldn't have made her come. Chance: It's not your fault, she wanted to come. Shadow: But it's my responsibility. I had a responsibility to Sassy, to love her and protect her. The same as I have to you... and to Peter. And the same as you have to Jamie. Chance: But we didn't ask for this job. Shadow: We didn't have to. It's built in. Has been ever since the dawn of time, when a few wild dogs took it upon themselves to watch over man — to bark when he's in danger, to run and play with him when he's happy, to nuzzle him when he's lonely. That's why they call us man's best friend.
It is a well-known fact that it is impossible for anyone who has ever loved any breed of dog or cat to watch this movie without crying.
Sassy and the birdwatcher. The man found a cat washed up on the riverbanks and, out of the goodness of his heart, fed her and took care of her until she could leave on her own.
Some may call it shmaltz and glurge, but the scenes with the little girl lost in the mountains are difficult to watch without shedding at least one tear of joy, especially when she and her parents are reunited.
The scene where she goes to Shadow. "Doggy?"
When Sassy is reunited with Chance and Shadow. note Gopher hole!
At the end when the kids and Bob are playing basketball and they call him 'dad'. That LOOK Bob gets on his face when Peter says, "Yeah, come on, dad" is adorable.
When Peter is going to the police station to get the cops to help them out, the officer offers an idea that helps them in the long run.
Another thing about Chance and Sassy's relationship — just look at the whole river sequence. Chance and Sassy are doing their usual routine of bickering but the second Shadow says Sassy's in the river...
Chance(running as fast as he can): Hang on, Sassy!
Chance(obviously worried): Did you find her? Where is she?!
Homeward Bound II: Lost in San Francisco
This exchange between Shadow and the pack of strays after he rescues a boy from a fire:
Dog: You know, you're pretty brave for a - a pet.
Riley: Brave, huh? Listen, you really think a human would do that for you?