We also log old and new values and the column they are from as well as the primary key of the table being audited in an audit detail table. Think what you need the audit table for? Not only do you want to know who made a change and when, but when a bad change happens, you want a fast way to put the data back.
While you are designing, you should write the code to recover data. When you need to recover, it is usually in a hurry, best to already be prepared.