Notts and Derby mostly run school buses using ex Trent Paladins and various ex London and Edinburgh deckers. They've also started running private hire contracts, using some seatbelted paladins and two ex trent coaches.
They also run contracts, mostly in Derby, the D1 as you mentioned, also the X17, 17, 17a, 9 and 35 and also some routes in Long Eaton and Ilkeston. They also run the 73 (Derby to Weston on Trent) comercially. These are run using a mix of Paladins, darts, a solo, a DAF myllenium, decekrs and recently a number of Centros have joined the fleet. Unibus branded buses also regularly make appearances.
They also provide all of the University of Derby's transport, including a number of routes to the Buxton campus (although some are now subcontracted to High Peak) and a network of three routes serving the Derby buildings. Excels, Paladins, 3 solos, 1 decker and 1 centro are branded for these.
Finally, this summer, Trent Barton subcontracted Notts and Derby two shuttle buses, both from Derby, one to Drayton Manner and one to Alton Towers. The idea was that you bought a ticket on a trent barton bus, made your way to Derby and the shuttle would take you to the theme park, and the ticket you bought on the first bus would also get you entry. Two double deckers were put into dedicated liveries, one sky blue for Drayton Manner and one dark blue for Alton Towers.
(They also sort of run part of the Ilkeston Flyer and Black Cat, that used to be run by Felix. Legally, these are run by Midland General but drivers were N&D uniforms and if the branded buses aren't available then N&D ones are used instead)