Mrs. Brisby's entire story arc is one giant CMOH. Not once in the entire film does she put herself before her family, especially her poor sick son Timmy, for whom she repeatedly risks her life in an effort to save his. The best part is that, throughout the whole ordeal, she remains terrified and fragile every step of the way, clearly showing that she would never in a million years have done what she's doing, without hesitation no less, had it not been for the sake of her own children.
Jeremy retrieving the medicine packet.
The "Flying Dreams Lullaby"
The moment where Jeremy the Crow finally meets the one True Love he has been longing for the entire movie (and she's a female version of him) is another moment of sheer awww.
As is little Timmy wanting out of bed (while his mother isn't having any of it.)
"Momma, I'm tired of bed, I wanna get up!" "Well... you're not getting up."
NIMH has quite a few, really. Especially concerning Jeremy. This crow has no real reason to help Mrs. Brisby, but he constantly endangers himself, even attacking Dragon directly to rescue her at one point. And his transparent but well intentioned attempts to allay her fears of The Great Owl later.
Mrs. Brisby: Owls EAT mice! Jeremy: Uh...Only after dark.
Him cheering up Timmy on their journey to Thorn Valley in the sequel was somewhat endearing, showing the guy at least managed to appeal to one of the kids (compared to the Epic Failin the first movie).
Auntie Shrew is set up to be arrogant and condescending, and all-around unlikable. Then when she sees Mrs. Brisby run off to sabotage the tractor while it's running, Shrew doesn't hesitate at helping.
With some hindsight, quite a few of Auntie Shrew's actions are rather heartwarming. When moving day approaches, she's the one going around to all the animals in the field and warning them the plow is about to start. She shows genuine concern when she hears Timmy is sick, she doesn't hesitate to help Mrs. Brisby stop the tractor, and when Jeremy tries to approach Mrs. Brisby's home, Auntie ties him up when she thinks he might be threat to the children. It's also implied that she's the one who is watching Mrs. Brisby's children while their mother is away and is clearly ready to go Mama Bear to defend them, even when Martin is a brat to her. In spite of her abrasive personality, she really does mean well.
At the end, when Mrs. Brisby mentions that Justin became the leader of the rats.
Seeing Martin back to his old self at the end of the second movie.