Is it OK to have more than one neutral wire in the same connection on the neutral bus bar on a main panel?
Neutrals must be one to a hole. No exceptions.

NEC 2011:


  408.41 Grounded Conductor 
  Terminations Each grounded conductor shall terminate within the panelboard in an individual terminal that is not
  also used for another conductor.


Since this is the main panel there is typically no separate neutral and ground bars, although additional bars that attach directly to the back of the panel box MUST be for grounds only. The metal panel enclosure CANNOT be used to carry current.

As long as both existing bars are connected by a link bar or other path you can use either side for neutrals. Grounds typically can be two and even three conductors to a hole, sized #14 or #12 and sometimes #10, and must be the same size. So if you need to make room you can double up on some grounds.

Neatness is all well and good, but fanaticism at the cost of convenience and logic is silly. Keeping the grounds and neutrals on separate bars in a main panel makes absolutely NO sense at all. IMO it is neater when all the wires don't cross from one side to another.