EDIT: This should be below JoshB's post, #12
But wasn't Neil's point exactly that Arthur Weasly doesn't have this education, and has no idea how electricity works? Most people are surrounded by electricity every day and don't understand how it works. Like magic is strange and fascinating and unexplained for us, electricity is for Arthur Weasley.If you've never had even the slightest education in physics then I doubt you'd have any idea how electricity works. I imagine he must have at least some working electrical items, if only a clock or something.
Clocks can be mechanical if you wind them up. Also, magic. The Weasley Family Clock is definitely magical.
Apart from that, you refer to the Quidditch World Cup Campsite as an instance where many wizards were in the same place over a stretch of time. However, this is quite remote, with only the Roberts Family possibly living there – and we don't even know where exactly they usually live. Most of all though, we don't know what kind of electricity they use there, and whether or not it worked during that time. The poor man was constantly being obliviated – do you think he remembers whether his radio worked in the evening?
Grimmauld Place is shielded from sight – I'm sure that it has some sort of shield that prevents the magic from leaking out, too. Possibly there are Ministry rules – if you want to start putting spells on your house (like the concealment charms in GP, or the household spells in the Burrow), you have to put up an anti-magic-leak shield.
I don't get the point you made earlier about giants and dragons. I can put my cheese in a plastic bag to keep it from smelling up the fridge, but if I put a mouse in there alongside it, it'll just bite a hole in the bag and get out, probably with the cheese. Magic itself and magical creatures are completely different things...