Okay, have to mention first off that I have no kids at this time, and my fiancee and I have no plans to have children. However, that doesn’t mean we have not discussed the what ifs, especially considering my enjoyment of all things horror.
First, I remember being scared witless as a child by films like Fantasia, Snow White and such. I think we protect our kids too much from spooky things, for fear it will affect them. And, while I’ll be the first to admit that the gore level in a lot of horror films is too much for a kid, I think some of the older black and white zombie movies are fine.
NOTLD is another matter. For one, it’s pretty intense for a kid. And, possibly most importantly, it has a very dark ending. Most of the movies that scared me as a kid had happy endings. The hero and heroine were together, the monster was vanquished (at least until the sequel) and order was restored by the ending credits. NOTLD, on the other hand, ends up with every character dying and society is on the brink of anarchy. Not exactly the stuff I think children should be watching until they are in their teens.
So, my suggestion (keeping in mind my non-parent but considering the possibility status) is to first, steer away from the gore. Too much body trauma on screen, no matter how unrealistic the effect looks, is not good for young kids. Personally, my potential kids won’t be seeing an R rated movie until they are in their teens, and only while I’m watching with them.
Second, keep the ending happy. It might not prevent nightmares, but the reassurance in the world being set right is comforting. Any movie that ends with the heroes dying should be reserved until they are older and have a stronger view of the real world (again, I’d hold off until early teens).
Also, watch the movie with them, or be nearby. I watched Psycho when I was ten on a late night television show. My mother stayed awake reading, in her room, and checked up on me at the end of the show. Very comforting, as I was crawling up the curtains when Mrs. Bates was spun around.
And finally, make sure it’s something the kid wants to watch. They have no interest in, or lose interest in after a few viewings. Don’t be the parent who forces their kid to be a football player/cheerleader/zombie fan.
Hope this helps.