I recently started a new job and had to have all of my tools calibrated. I had a 0-3 set of CHEAP Chinese mics, plunger indicator, and a test indicator that are well used. They passed calibration with flying colours. My 6" Starrett caliper and mitutoyo .004/.0001 test indicator, did not. Big name doesn't always mean better, it depends on how the tools have been treated throughout their life.
My suggestion would be to CLEAN your caliper. I've had digis start to screw up and not repeat when they got dirty with coolant or oil. I would have given them a good clean with some contact cleaner on a q tip before adjusting the screws. Give them a good clean, and readjust so that they read 1.000^0 on a 1" standard, then as suggested test them on 2", 3", 4", etc. Test all the way to its limits. If you don't have standards out to 6 or 8 inches, whatever the caliper size is, you can use other objects of a known size, such as setting rings for inside mics, or just pieces of rod that have been measured with a known good tool.