Some of our customers believe that JIRA should implement a similar functionality to the Confluence one - CONF-11554.

The standard 500/server error page displays large amounts of information about the server. While this is very convenient for troubleshooting, it's a problem in environments where security is a major concern and it's important to provide as little information as possible to potential attackers.
We can, and currently have to, ask customers to customise 500page.jsp themselves. However, it should be easy enough for us to include an alternative version which simply shows the following:

CONFLUENCE
System Error
A system error has occurred - our apologies!

Please contact your Confluence administrator to create a support issue on our support system at http://support.atlassian.com with the following information:

1. a description of your problem and what you were doing at the time it occurred
2. attach the application server log file (if possible).

WORKAROUND:

If you want to remove information from 500 page, follow this guide:
https://confluence.atlassian.com/display/JIRAKB/Remove+information+from+the+500+page