Calipers should always be stored horizontally. Using oil on a rough caliper will only attract dust. Clean a caliper with a lint-free cloth and proper cleaning solutions. Dial calipers sometimes will have their gearing mechanism jump a tooth of the gear rack, because of dirt or chips. This causes the pointer to be offset by several degrees.
Users often try to rectify the situation by resetting the gearing mechanism themselves.
Instead, have the caliper repaired by a qualified repair laboratory. And, never measure parts being rotated, such as those turning on a lathe. Calipers used frequently or in harsh environments require shorter calibration periods, as do gages subject to unusual wear. The movement should be free of rough spots. Remove surface imperfections with a hard Arkansas stone.