I just had a look at the form on the backend, and you have a huge number of plugins running - about a dozen email and three PHP, and the PHP ones are running about a dozen database queries.
I think I've fixed it for you. You had quite a few errors in your code. I think the one that was causing the problem is you were running $db->loadResult() on update queries, which is wrong. You only use loadResult() to fetch a result from a SELECT query. For things like insert, update and delete, you need $db->execute().
Are you sure this stuff ran correctly before you updated? I'm kind of surprised that it ever did.
Anyway, I don't know if the plugins are doing what they are supposed to do, you'll need to check that, but at least the form now submits without blowing the database up.
-- hugh