The movement should be free of rough spots. Remove surface imperfections with a hard Arkansas stone. Check the carriage for excessive play. Check the zero setting. Vernier calipers sometimes offer adjustable scales.
Dial calipers have dials that can be rotated, and electronic calipers offer floating zero.
Check the caliper for accuracy using gage blocks or a caliper master. Check the external jaws for wear by using a precision ball or pin. Check the caliper's internal jaws with a gage block stack and jaws or caliper master, in at least two locations. Do not use ring gages. If the caliper has a depth rod, check it using a gage block.