Personally I have no problems with Dark Matter, there is ample evidence that there is mass galaxies that we cannot see.
We use dark matter to explain motions. Right now we only have Keplerian explanations, but we do not know for certain that other rules do not affect objects, especially on large scales. If we assume that no other laws other than Kepler's control these motions, then yes indeed, there is ample evidence for dark matter.
Dark Matter is predicted by using a half-way house set of techniques between Newtonian Gravity and Linearizd General Relativity.
I've never heard of Kepler's Laws being used except in multi-galactic simulations.
  