Sorry guys for the long waiting time - I'm also just a vlouteer here and sometimes things are growing over my head.
The problem is that the date entry '0000-00-00 00:00:00' is wrong. It should be NULL. Somehow the conversion did not work during the update.
To solve this issues you will have to touch the database with phpmyadmin or similar.
There find the table 'PREFIX_jem_categories'
Then find the field 'modified_time' - according to your error message its value is '0000-00-00 00:00:00'
Click in the field and select the checkbox 'NULL' (to apply the change make a mouse click outside of the date box)
I hope this solves the issue