RM, I have a hand-held body fat monitor and I'm absolutely convinced that all it does is record the age, sex, height and weight data you put in and do an elementary calculation based on a pre-programmed formula. I don't believe it measures anything. It comes in useful as a sort of adjunct to reinforce what the scales are saying when people start whimpering about "heavy bones" and "well, it's all fluid retention and it's your fault for not giving me water pills", but as a scientific device it's a confidence trick.
Officially, underwater weighing is the most accurate way of assessing body composition. Calipers are next best, but only if used properly - and in the gym they frequently aren't. The Tanita stand-on thing has been shown to be capable of an error of up to 5% in some tests.
Body composition changes gradually, so a measurement every couple of months is plenty - in fact, like the scales, they can probably be dispensed with in favour of the honest, no-nonsense, no-science "wobble test".
Cheers, V-rap.