Spoiler: show
In discussing the peculiar electromagnetic properties of Hogwarts on another forum, I've come across two theories that are actually pretty interesting.
The first comes from the question of why Hogwarts affects electronics so greatly, when we've never heard of any Muggles living near Diagon Alley, the Ministry, or St. Mungo's having any such problems. All are places where magic is both passively and actively being used and by large numbers of people. This would naturally lead one to believe that such places would also have a lot of "magic in the air," to quote Hermione. Why is it, then, that they seem to not have any of the effects of Hogwarts? My theory is that Hogwarts is built on or near a natural wellspring of raw magic. Unlike channeled, purposed magic, raw magical energy is chaotic and interferes with Muggle electronics because of its unpredictable nature. Channeled magic doesn't have this problem, as it makes the magical energy more coherent and, unless specifically made to do so, wouldn't naturally interfere with electronics. This could also explain why such places are comparatively rare, as magical wellsprings make it easier for students to use and manipulate magic; they use less of their own power, and exhaust themselves less often, an ideal learning environment for young mages.
The second comes from why things like ground-penetrating radar can't discover places like the Ministry. Making the whole place Unplottable would help, but it wouldn't help if a group of Muggles were, for example, digging a subway tunnel and accidentally broke into the Ministry. How is this prevented? Places like the Ministry and Diagon Alley are actually contained in large pocket dimensions. I like this one because it turns a mere handwave, "a wizard did it," into a nice bit of Time Lord-esque dimensional engineering.