I guess it all depends on the airfield/dz layout. Where I instructed (Sibson), aircraft and parachutists were kept well apart as the DZ is distant from the runways. The main danger was that referred to above in megan's post, when pilots didn't read their notams and infringed the active DZ airspace at varying altitudes. Quite a few close calls over the six years I was there...including a fast jet from an airfield just to the north...