I drove a 1996 D1 for 5 years and about 80k miles (105k on the clock but previous owner put the first 25k on it). I've had my 2004 D2 for about 1.5 years and 16k miles (bought it at 50K miles).
Problems with the D1 included leaks everywhere (oil pan, rear main, hub seals, rear diff, steering box), steering box went bad, rotoflex wouldn't last in the rear driveshaft (after about 2.5-3" of lift), and the brakes always sucked. The engine always hummed along fine but it was incredibly weak on hp and torque. I'm sure I'm forgetting a lot of stuff but overall the D1 was a really a piece of shit. But I loved it.
Problems with the D2 are more annoying, including fucked up windshield wipers (intermittent only works intermittently - still have to work on this), broken window regulator plastic wheel (fixed it with metal washers a few days ago), a dash light is out and the rest are flickering (still have to work on this), leaking throttle body heater (repaired), leaking valve covers (which killed an O2 sensor, all repaired), completely unreliable front driveshaft (replaced with Tom Woods shaft), and of course the 3 amigos that Land Rover somehow got away with avoiding a recall on (it's my shuttle valve which I might one day getting around to fixing with the wiring bypass trick but no way I'm blowing $1,000+ on it). The engine runs strong (4.6 is still pretty wimpy but so much better than the pussy 4.0) but the engine has that annoying tick. No one can figure out why these trucks sometimes tick along like sewing machines but seem to run finr. The brakes are great since I finally did it right and went with DBA's on the front axle. So, you see, the D2 is pretty much a piece of shit too. But I love it.