I took a Bod Pod (air displacement) test last month, and that exact same day I met a guy in the gym who was using a handheld electrical impedance tester - they were within 1% of each other, so they're pretty accurate. However, once you get past a certain percentage, the testing range definitely widens with hydration. I agree about the rolling average (I'd say average a week of measurements, all taken right when you wake up and before you drink anything). The doc who ran the Bod Pod said that calipers are good at lower percentages, but on some larger people you may get a reading that is off due to internal fat storage (that was my case).

If you use calipers, it may be a good idea to track your fat loss not by trying to calculate your percentage each time, but just writing down the numbers you get at each site. As the numbers go down, you'll know you're losing fat. I have a set of calipers (about $15 on Amazon) and I use them about once or twice a month just to track progress. Once I lose about another 50-60 lbs, I'll go back in for the Bod Pod for an actual reading.

I used to have an electrical impedance scale, but its weight limit was too low. So I had to stop using it - I like my calipers for just spot checking, and the Bod Pod is my twice-a-year check.