When I first watched this film, what really left me stunned was the technical execution of the animation; in particular, the attention paid to gravity and wind effects.
There's a quick shot early in the film where Sally is following Jack through the graveyard. As she darts between headstones, her hair billows behind her as she runs.
Then there is the scene of
Poor Jack in the graveyard after Jack has been shot down.
Watch the tatters of Jack's suit as he moves. For me, this showed how much (at the time) stop-motion had advanced when the animators could pay attention to such details. (For all their artistry in their own day, neither Ray Harryhausen nor Rankin/Bass went to that level of detail.) Animators often strive to keep characters simple just so there isn't too much detail to have to animate. In Nightmare they seemed to want to push the other direction.
As for the soundtrack, Oogie Boogie's number was always my favorite.
It's much more fun, I must confess
When lives are on the line.
Not mine, of course, but yours, old boy,
Now that'd be just fine.