What tables are used for civicrm reports?
4.2->4.7 is a huge upgrade. Swathes of tables - including Activities and Settings - have changed. If you have any custom reports or extensions these definitely will need to be upgraded without a doubt.

This could be caused by a number of things.


Is this all reports, or just some? What are the names of the failing reports?
Please could you provide a screenshot?
Have you looked in the CiviCRM error logs and the Joomla! logs?