It is great your checking your credit ahead of time before you start searching for your next home. You can get a free copy of your credit report from each of the reporting credit agencies once a year. Look for any items that are not correct and fix them by reaching out to the creditor or the reporting agencies. Here is a link to all 3 http://www.markknowshouston.com/buyers_roadmap_02.php
As others have mentioned, they have ways to resolve items that are not correct, but you have to start the leg work by reaching out. Plan 60-120 days to get these items resolved. A lender can also assist you with some of these items as they work with the credit reporting agencies every day. Good luck and let us know if we can assist you here in Houston.
Call ONE of the Credit Bureaus and "dispute" the balance. They will send a letter to the landlord to verify the amount owed. If he does not respond within a set time, it will be removed. It is fairly common to find old info on your credit reports that are easy to clean. Just takes a little effort and should not cost you a dime!