I doubt the GP was thinking of this, but there exist some interesting side-channel information attacks using the electricity grid.
(disclaimer: I am not very knowledgeable about electricity/electronics, so forgive me if I'm a bit hand-wavy or wrong about the details)
The actual electricity output from a wall-socket fluctuates continuously by a tiny bit over time. I suppose this goes for both the exact magnitude of power output (is that voltage or amperes?) and the exact frequency being ever-so-slightly above or below the expected 50Hz. These fluctuations can be measured (or fingerprinted) by carefully measuring the output of electrical appliances, such as the crackles and pops in audio recordings or brightness of light bulbs, and in fact many other things.
The other important fact in this trick is that apparently these fluctuations are all the same over the entire grid (or subsections of it, I guess, depending on network layout). They are also pretty much random. This means that if you keep a log of these fluctuations over time, you can timestamp recordings of pretty much anything with extreme accuracy, by matching up the patterns of crackles or power fluctuations in the recordings to your logs.
This would then allow one to detect fake call logs, video/audio cuts and splices, stuff like that.
It's not a gigantic privacy risk (therefore probably not what the GP was thinking of), at least not from the applications I can think of the top of my head. I do love side-channel attacks like these, though. They're always so clever and out-of-the-box :)
What is that supposed to mean?