I certainly wouldn't mount anything like an iron sculpture above my bed, but beyond that, I think it's mainly common sense & using the correct mounting hardware for anything you want to hang to minimize any potential hazard.

Nothing you can do about earthquakes, and if you're in the "zone", things are going to fall, break, crack, and possibly collapse. There's really nothing you can do to to avoid it, other than keeping absolutely everything on the floor. Everything!

Depending on the type of earthquake, consider that items can be thrown sideways in an earthquake, so the heavy vase on a nearby dresser is can be deadly when it is thrown horizontally across the room. Also out - the heavy mirror above the bed. It is just better to keep things simple and uncluttered in the bedroom where you don't have a chance to move for cover. The most serious injury came from the floor to ceiling brick facade surrounding a fireplace that fell forward in one piece and crushed the boy sleeping 5 feet away. These are issues that need to be considered.

Old brick fireplace chimneys are my biggest concern. I wouldn't let anyone sleep near a fireplace or a chimney.

I also have some art hanging over a few of the beds in the house, but never a piece with a heavy frame or glass. I only hang canvases stretched over a lightweigh wood frame.

I also don't buy large heavy pieces of furniture, especially for a sleeping room.

Two story wooden houses do a great job of rocking with the earthquake and returning to their original place.....broken windows might be expected and furniture does get flung around.