From my experiences of travelling around this country, and we have been doing it for a long time, just use common sense, if it doesn't feel right, don't do it, you get the feel for a place pretty quick.
However we have not had any bad experiences over this time, secure your stuff safely and all should be fine.
As for Uluru, and as been mentioned you cant just camp anywhere you like unless out side the area itself, one isn't even allowed to get off the designated roads and tracks in the park.
Leon
