Well, two things occur to me in response to that.

1. It behooves one to go through all of the store's functionality to make sure things are working, before opening to the public. This includes creating accounts, adding products, placing those products in the cart, and completing checkout with the payment gateway you intend to use. And then optionally refunding the transaction if it's appropriate.

2. Email system error messages are enabled by default so that you, the shopowner, can see all those messages first-hand when they occur. You can disable that by switching the "Friendly Email Errors" option on in Admin->Configuration->Email Options if you so desire.


As for a generic "sorry, we encountered an error" page, that's not a built-in option at this point.
There is a general PHP-Error debug logging utility in the free addons area that can be used to collect PHP errors for the storeowner to review from time to time, which may be of some related value to you.