With some groups, the issue is that they make such a total statement that influence risks becoming pale imitation - comical, redundant or both. Joy Division, Ramones, The Smiths, Portishead: all fall into that category. Massive Attack are a much better influence than Portishead precisely because they're not given to coherency - think of all the forgettable second-tier trip-hop acts who cloned Dummy rather than Protection.
Then there are the bands whose would-be disciples simply don't notice or disregard the ambiguity in the original work. A great example of this would be Blur circa Modern Life Is Rubbish or Parklife: Anglophile records, but also profoundly critical of British culture, as The Kinks were before them.
Take away that complexity and you merely replicate the past, offering musical pastiches of a particularly thin slice of British (or, rather, English) identity without nuance or comment.
Finally, there's the 'you only get away with this in the first place because you're so darn good' category, with inferior imitations having few of the merits and all of the flaws. Take Led Zeppelin - no band who has tried to sound like Zep has ever come close to being as good as them. And that's despite the occasionally reactionary sexual politics and the musical and other over-indulgences which would have artistically hamstrung a lesser band.
Over to you? Any other examples of great bands, bad influences that spring to mind?