FYI, I opened a ticket on this. The first step towards partial resolution is to upgrade from 7.
5 MP1 to 7.5 SP1. This is supposed to aleviate the issue of not being able to see the classification after the problem has been worked. As to the reporting this is the suggested workaround below
"In 7.5 SP1 we have figured out a workaround for your reporting issue we worked on.
Edit a report and on the left under Problem Management add Custom Problem Management then on the right you will see Classification."