This also occurs with highend audio systems often annoying to audiophiles. First, make sure the Mac Mini is conected to a grounded outlet, preferably via a protected power surge unit. Grounded outlet testing can be verified with a $2 tester from any hardware store.
Secondly, make sure no other appliances are connected to the same outlet or circuit as the Mac Mini. Switching other electrical units on or off which are on the same circuit can cause audible electrical interference. The Mini's connection should be isolated from any non computer-related appliance or electical gear on the same line.
I'm not saying this'll fix the problem, but at least eliminate sources that could cause this.