BMI goes up the more muscley you become... which is why the table rates well toned athletes and bodybuilders as "obese". It's a fairly poor indicator of health and fitness when applied to individuals, since it was never designed to do that. (BMI was created as a tool to assess the generic health of very large pools of people for insurance purposes, but it breaks down in smaller pools and even more so on individuals).
Home scales that measure body fat % are, as the previous poster mentioned, very sensitive to water, and they can only measure your lower half since they send the current up one leg, and down the other. So, if you carry your weight unevenly (like everyone does), it won't be accurate. If you lose 10 lbs from your belly, back, and arms, and none from your legs, the scale will tell you that while you lost weight, your body fat % is now higher! Silliness :D
You're losing inches, so you're doing it right. Sometimes when you get fitter, you lose inches and not pounds, so that's ok too!