In short, probably not. Unless the trainer at your local gym has logged hundreds of hours using skinfold calipers and was TRAINED PROPERLY, you likely got a bad job there, as well. Accurate calipers cost hundreds of $$. Skinfold measurements must be taken sequentially from 3-4 spots (subscapular (under the shoulder blade), back of the arm, just above the hip bone and back of the leg (hamstring area) are good spots) and non-repetitively, meaning if you take 2 back to back measurements from the same spot, the fat can compress and give an inaccurate measurement the second time. Phil is correct about underwater weighing (hydrodensitometry). Go the a local state U and they will likely have studies going on where you can get these things done for free. Hand-held and floor bioelectrical impedance machines are bologna. They can give you a consistent measurement but usually not an ACCURATE measurement. This method can be accurate if performed by a qualified exercise specialist or physiologist. When done properly, you are hooked up to various leads, kind of like an EKG, for more accuracy. There are also a host of prerequisites for the impedance test (urinating within 30 minutes of test, no diuretics, not during menstration for women, no caffeine for 24-48 hours,etc.). Bod Pods and DEXA scans also produce results nearly as accurate as underwater but can be expensive and they are hard to find. Just use the old fashioned method. If your clothes are fitting better, you are losing bodyfat. Sorry for being so technical, but my PhD is in clinical nutrition with a minor in sports nutrition/exercise physiology. Take it easy.
"He's like a man with a fork in a world of soup". Noel Gallagher of Oasis, referring to brother Liam