First and foremost, make sure the pond is well constructed. Check all around for signs of leaking...past or present. Look for trees and/or brush on the dam. Large trees can be a problem to the integrity of the dam and small trees and brush should be removed. Check for signs of animal damage...nutria, beaver, or otters, etc. Look for holes in the dam just below the water line. Check the spillway system or pipe system if it has one to determine the condition.
Check that it has adequate run-off to feed the pond and also that it does not in any way endanger someone downstream from you.
After checking the structure, then check out the bottom of the pond, if you can...determine how much muck is present and if resulting water depths are adequate for your needs and weather conditions.
Finally check out the fish...but you can change the fish and fix any problems that may be present with over/under stocking, etc. much easier than you can fix a serious structural problem.