Hi PipingHotSoup,
The issue with bodyfat measurement is that accurate measurement is virtually impossible and the closest we have to really accurate requires techniques like hydrostatic testing or Dual Energy X-ray testing (needs expensive specialist equipment that is usually only available in certain hospitals and universities). Since this isn't readily available to most of us we're left with calipers or scales, (both better IMHO than the very rough estimates available from formulas based on two or three measurements of body circumference at various points).
Even then, calipers and scales are sensitive to the particular brand/quality of the equipment and the technique used with calipers and conditions in which the measurement is taken with scales.
I think the best rule to follow, whichever method you choose, is don't worry too much about comparing with others as their body composition will almost certainly have been measured differently in some way to yours. Also don't measure too often or get hung up on anything beyond the decimal point (the equipment is simply NOT this sensitive).
If you're using calipers repeat the test a number of times using the same skinfolds and being absolutely accurate about the distances/points used for measurement and always use the highest quality (read most expensive) calipers you can get your hands on.
If you're using scales put them in the same place, measure at the same time of day, and make sure the contact points are as clean as possible.
Others may have more to add on this and all this is just the findings I've made from personal research and the advice from numerous people I work with who are involved in sports science or have studied it extensively. Google it and be aware that many sitesare thinly disguised sales sites for a particular brand or other of body fat measuring equipment. They may have some sound advice but they'll also tell you their product is the ONLY way to accurately measure bodyfat.
This site explains the various methods fairly well:
http://www.new-fitness.com/body_fat_analyzing.html (note that BIA or Bioelectrical Impedance at the foot of the page is the method that bodyfat analysis scales and the handheld OMRON machines use).
Hope this is some help