A well-soaked stamp shouldn't have paper traces on the back. Regardless, it is customary to take more than one measurement in different parts of the stamp. If done correctly, the measurements should give you a tight enough range to determine the thickness.
Take Albert's example above. If you consistently got measurements greater than 0.0034 inches and less than 0.0037 inches you need to start looking for errors. It could be gunk on the back of the stamp, a mis-calibrated micrometer, operator error or a combination of the three.
I found a well done repair on an 1843 Brazilian Bull's Eye stamp because I kept getting a clunky measurement on one part of the stamp. Sure enough, there was a patch.
It takes practice but the method works well.