What is the most useful strategy when your application throws an exception in the middle of the demo, in terms of keeping the client's mood still positive?
If your client doesn't trust you, there's nothing you can really do. I build trust with my clients so when something like this happens, they believe me when I give them an explanation. And when I tell them what I'm going to do to prevent future problems, I make sure to follow through.
Depending if this is a "final" demo or if its a mid-project demo will also affect whether you can really alleviate the customers' concerns. There's very little you can do to make the customer happy if it's the end of the contract and there's no more budget for testing and bug-fixes.
One generic strategy I've used: if you have someone in the room document the exception/problem in front of the customer and let them know it is going into the bug tracking system for investigation and testing, that will demonstrate to them due-dilligence and alleviate some concern. You, of course, need to follow through and make sure to fix the problem.