Be absolutely certain that your prospective disc jockey owns music that's appropriate for your event, and is willing to play only that music. Certain songs shouldn't be played for little kids, or at weddings. Sit down and discuss this issue with them before they every play a note.
Go with your gut when hiring a disc jockey. If they don't come across as professional, or you simply don't develop a rapport with them in person or on the phone, choose someone else. You may be noticing something on a subconscious level that could affect your event.