http://www.gigamonkeys.com/book/beyond-exception-handling-co...
Notice I'm not saying you should go and program in Common Lisp, just that you should understand those ideas before you engage in any sort of meaningful discussion about exceptions, errors and error handling in general. Because, you know, some things have already been thought about and invented. Don't re-invent them.
And on a more practical level, in languages with dynamic binding it isn't difficult to provide error handlers and "send" them up the call chain, so that in case of an exception your handler gets called, fixes the problem, and lets the called function continue. You can do all that using try/catch as a low-level tool, I've seen it done in Clojure, using JVM's exception system.