As more and more people are switching homes and establishments on a regular basis, be sure to try rekeying your locks on the regular. When someone has sold their house, that means they have knowledge of how the house works and have frequently used the keys that are now in your hands.
If they are going to be giving you these keys, the then chances are that they are in possession of duplicates as well. Even if this isn’t true, do you really think you’ll be able to sleep easy knowing that they could potentially enter your house at will?