I wonder why everybody is convinced that Dumbledore doesn’t want to have his want checked or even seen. All the instrument would say was that the wand was made from elderwood, right? And we know THE elder wand wasn’t the only wand made of elder. In DH Ron says about elder wands something like “wand of elder, never prosper”.
The instrument also states the time the wand is in use. This might cause a problem for Dumbledore, because this elder wand has been in use for hundreds of years. Though it is not uncommon for wands to be passed on to others (isn’t Ron’s first wand an old wand from one of his brothers, like his pet?) hundreds of years seems more than a bit unlikely. However, Dumbledore has only been using the wand for a shorter time. So the real question here is: does the instrument say how long the wand has been in use, or how long the user uses the wand? That answer would tell us whether Dumbledore would avoid these instruments or not. On hiding the wand from other people, nobody really knows what ‘the deathstick’ or ‘the elder wand’ looks like apart from its previous owners, right?
Dumbledore wouldn’t have to hide and switch, but I like the idea that he could switch when performing magic he feels more comfortable doing with his own wand, if any.

Similarly picture-Percy may have moved between the picture in Arther’s office to a picture at the Burrow and again felt the tension when his family talks about him. (or lack of talking about him!)

Another random side-note about picture’s ability to move between paintings in the same building… How come none of the more. .. erm…interesting… picture subjects are ever sharing the frame with the headmaster/mistresses in Dumbledore’s office? Is there a level of picture-respect that you don’t enter someone’s frame unless invited?

I’d also say that as long as the letters are on the phone in the phone booth, it might not matter whether wizards have heard of it before – they could simply figure it out :)