Handling errors is easy and hard, depending on how much information you want at runtime. Any exception thrown in a call to a property or method is converted into a LV error w/ error code 1172. The information on the exception is then put into the error text, which is okay for humans to read, but I don't recommend writing code to try to parse it (at a minimum, we don't say that the format may not change in the future). Unfortunately, there isn't a way to get the exception object currently.
Therefore, you might want to think about saving off the exception object yourself (wrap your methods w/ a try/catch and a rethrow in the catch) in the object instance and expose it as a property. Thus you can access it via code at runtime for error handling cases. This, of course, assumes the server is either single threaded, or you'll use TLS (thread local storage) to store off the exception for the last method invoked.
Anyway, those are some initial thoughts on the matter. Feel free to reply w/ comments or questions.