My best friend owns a '01 LR Discovery. He too has heard if its dubious reputation (almost as bad as the early MLs), but I believe the millenium models have for the most part been devoid of the reliability issues of the late 90's series.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car