Hi Scan and all,
These guys are guessing, Hoofy comes close but I have the experience. (;->) The clicking you hear is a pulse train coming from the other's scan control for the most part. Some loud pops can come from it's local oscillator, part of scan control but in any case that's the source. The interference can be radiated, conducted or both, conducted along the coax sheld if they're coupled to a common antenna or through the power line, radiation speaks for itself.
Your specific solution if it really bothers you depends on your radio environment, I have given you sufficient clues. Take note that plugging it in a different outlet may not solve the power line conduction problem as often all in the room are connected together and sometimes those in another room are also on the same branch.
A scanner is a Part 15 device so some spurious emissions are to be expected within limits specified by the FCC.