EMP wouldn't be the problem to worry about.

I'd be very concerned about the resonance issue. When you have such an isolated body, with a dead core whose only major oscillations are in the form of metorite strikes - how will an atomic detonation reverberate? With the weak atmosphere and gravity - what about the possibility of losing lots of chunks of the tough moon rock to space and possibly interfering with satellites or creating a minor "ring" of debris around the moon? Also - the sorts of nukes we'd likely be testing would be far removed from the "Fat man" or "Little boy" variety, likely much more powerful and problematic.

Too many questions and too many risks. If I wanted to test nukes I'd try the larger asteroids, and avoid any hassles.

The moon is a sweet place to LAUNCH nuclear missiles from though. It might make sense to use the moon as a launch point for any future planetary defense system and I'm certain is viewed as a great place for a US ASAT and US space "domination" system.

SDAI-Tech1