I agree that to really resolve a client's complaint you'll probably have to take it offline, but I wouldn't take it offline entirely. I would defintely respond online first with a genuine apology, and a promise to contact them with the intention to make it right for them (regardless, of it you think they're right or not). Also, I don't think that we should be so afraid of complaints online. Not if we're paying attention. Studies have shown that a client complaint handled well can actually improve that client's loyalty. Not only will that client have a strong story to tell others, but when you do address it online, it lets prospective clients know that you're a firm willing to acknowledge and rectify mistakes.