How close must you be to true level to not harm refrigerator

Bordercollie wrote:
I wonder how much effect, if any, there is in operating a modern fridge, in hot weather, slightly off kilter, for extended periods, without driving.

How slight is the slightly off kilter?

If it's well within the spec limits for the fridge, it should be perfectly fine. If it's well outside the spec, it's not fine at all. One degree off level won't cause any problems; the pipework has enough slope that the fluid still flows properly by gravitation.