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).