Can paying old debts hurt your credit score? Yes.
First off let me tell you I believe in paying all your debts on time and in full. I believe this for moral and legal reasons, so this post is not away to validate not paying old debts.
So here is the issue. If you have old debts that are delinquent, charge offs, or in collections and pay them off in full this can cause your Credit Score to drop drastically. Why? Because the payment on the old debt will actually update the negative marks on your credit report? It could inspire a new round of collection.
Some people advise you let the statue of limitations run out on your account and hope your score goes up because the account is no longer showing on your report. Others say you should, and have a moral obligation to pay your debts no matter the impact on your credit report. This is a personal issue each person has to make for themselves.