In my company's contract, we limit our liability to the amount paid by the client. Without a liability limitation clause in the contract, you're taking on a potentially unlimited amount of liability in each project. It's not worth the risk. A few good paragraphs in the contract make all of the difference in the world. If you don’t have a liability limiting clause, you should.

Also, this client engagement started going wrong from the very beginning, when the team allowed so many changes for free, and even launched the website without final payment.

I'm all in favor of over-delivering -- and I probably also would have fixed the problematic PSDs for free -- but 294 hours of work on a 116 hour project, launching the website without the required final payment, and then continuing to do work is way too much.