Is there some way to wrap the entire page in a try/catch, so that I can catch any error from any script that is executing?
Turn on the debugger and break on error.
You don't want to catch every error in the entire page on production code. That's horrible.
Use window.onerror instead of a big try/catch.
You could actually do some useful things in the error handler, like posting the error information to your server so you know when things are breaking on your page.