To correlate orders and payments on PayPal, you can use the order id which is specified in all the PayPal emails and in the PayPal transactions. The transaction number is indeed not stored in the order information with the PayPal plugin but it would be easy to add. It's just that no one told us that this was a problem so far.
I have found (from my experience with Virtuemart) that matching up orders to paypal payments can be a real pain - Joomla usernames/names often don't match names in Paypal and often its a matter of looking through 5-6 possible matches to find the correct one.
Our event registration component has a couple of native payment engines and one of the features of the component and these plugins is a linkage between the order and the payment engine transactions/activity. The plugins generate the output/links (which are payment engine specific) making it easy to view all the payment activity related to an order directly from the order detail page. Direct access to log messages would also be good. An invoice/payment receipt generating system could also tap into these plugins to include payment defails in an invoice/receipt.
I think incorporating this feature would be a good idea - personally I am not happy to
rely on an email notification of a cancelled/reversed payment especially for virtual transactions (downloads and other non-physical delivery items). Emails get lost, they get read by a different person to the one processing an order etc.
thanks
Geraint