How can you tell if a battery has been damaged by under or overcharging?

The only way is with a load test. Use the same procedure for VRLA batteries that you would use with a flooded cell battery:

   1. Recharge if the open circuit voltage is below 75%
   2. If adjustable, set the load at three times the 20 hour rate.
   3. Apply the load for 15 seconds. The voltage should stabilize above 9.6 volts while on load.
   4. If the battery has a CCA rating you can apply a load equal to ½ the rating for 15 seconds. The voltage should stabilize above 9.6 volts while on load. To apply a more determined test – if your load tester has the ability - you may apply a load equal to 100% of the rated CCA for 30 seconds. The voltage should stabilize above 7.2 volts while on load.
   5. If below 9.6 volts (7.2 volts for the 100% CCA test), recharge and repeat test.
   6. If below 9.6 volts (7.2 volts for the 100% CCA test) a second time, replace the battery.

NOTE that for the above tests to be completely accurate these tests should be performed with the battery temperature being stabilized at -18˚C/ 0˚F.