My breaker panel has several available slots that I want to use for additional circuits, bus the neutral bus bar is almost out of available holes. An electrician previously put two ground wires (12g or 14g) in one hole and this looks fine to me as the hole is plenty big enough and the set screw is plenty strong enough to clamp down on multiple wires at the same time. Is there any reason I should not do more of this? Is there any reason I should not put two (white) neutral wires in the same hole?
You should not put two wires on one screw. The reason being is that if you must disconnect one you will be loosening the other which may have a load on the neutral. If it is a ground, you need a continouus path to ground uninterupted by removing another device. You can probably put in a ground bar kit available at supply houses and home centers. There are probably threaded holes in the panel available for this. Then you can put your grounds on the ground bar and free up your neutral.