Is old balsamic vinegar healthy to have in salads?

Generally yes. I know that when I go shopping for balsamic vinegar the ones that have been aged for 5 years cost more, and the ones aged for 10 years even more, suggesting that, like a fine wine, the flavor gets better with age. So as long as it has not gone rancid (which you should be able to tell by its tasting bad), old balsamic vinegar is perfectly fine to have.