Issue number one you've already got; improper grounding. The entire audio system should have a single ground point. Traveling shows manage this well by using a distro, and running power to the mix position by a long cable alongside the multicore. Installs often want to use sockets on the wall, and then the electricians get involved, and thats the end of the single point ground.
Issue two is high impedance and/or unbalanced signals. If you have an unbalanced source and it needs to travel some distance, balance it with a DI box. Everything on stage should be a balanced source to the mixer, either naturally balanced (eg SM58) or go through a DI.
Issue three is a variation of issue two, equipment built into plastic boxes.
Laptops are a nightmare and seem to be getting worse; use a passive transformer isolated DI box, the lowest cost one I know of is the
EWI FDB101, which I use myself and is a great hum lifter. It may not be the highest quality DI box, but I'll trade losing the racket that laptops make every time. With computers in general, an external USB or firewire connected audio interface is better than an internal audio card, and much better than using the speaker output...
A low impedance balanced audio cable like goes from a mic to a mixer is almost impossible to get buzz into. The multicore returns to the amplifiers are even harder, as the signal level is so much higher.
Things that don't make an appreciable difference - using separate power, using different phases. If this does make buzz go away, it's just telling you there is still a fault to find.
Finally, persevere - you can make your audio system bombproof.