The equations were developed based on normal weight people. Applying them to people with excess fat may be inaccurate. Some measurements cannot be done without the help of another person. The amount of tissue picked up to form the skinfold can vary. You get different results depending on how hard you pinch the fold of skin.
More expensive calipers are more accurate.
If a different person takes the measurements each time, they may not be accurate or consistent. Proper technique requires training. Even under the best of circumstances, individual differences in measurement techniques are common.