I think the most important thing is consistency. Always use the precise same point, pinch the same amount of skin, and at the same angle. But, I feel that the "single site" measurement method described in the AccuMeasure instructions isn't the most accurate. There are other, multiple site, methods which I believe give more accurate results and are especially better if you don't store body fat evenly over all areas of your body. The down side to the multiple site tests is that you usually can't do them yourself. Measurement sites such as tricep, subscapular, axilla, etc. are difficult/impossible for a person to measure on themself. But if you have someone you can do measurements with, try this site:
They have nice 3-site and 7-site calculators for men and women that make the calculation part very easy. It shows precise areas to measure and which direction to pinch (vertical, horizontal, angled). I also like the way it requires three measurements per site, so it can average out the measurement variabilities that you are concerned with.