This tip may seem overly simple, but I see this mistake all the time when editing. We're used to using who and that interchangeably when we speak, but the rules of writing are less forgiving.
Always use who (or whom) when a sentence refers back to a person. Use that when talking about an object. For example, "Mrs. Smith is the librarian who helped me find my research books." Or, "His blog is the one that I read every morning before work."