No, No, NO, NO, NO! This is NEVER desirable in production for any reason at any time. Having this is production is a major security hole. Let's say the error is a SQL error ... now, you're displaying your database schema to the world. This means that I can craft a query to perform a SQL injection. And, that's just one of the millions of ways to break your site.

Instead, it is much better to redefine the 500 handler as a script which displays a generic "There is a problem. Please contact management and let them know what you were doing". The error should be logged in some datastore (such as the error_log, if you're using Apache) and every page view should be logged, including user and parameters (which the access_log doesn't necessarily have), so that support staff can replicate what the user was doing at the time of the error.