Is a biennial flight review valid for any airplane category?
Yes.  61.56(c)(1) calls for "an aircraft for which that pilot is rated."  The reg does not require a review for each category/class.

And as further confirmation, AOPA's Pilot's Guide to the Flight Review specifically states:


  The satisfactory completion of a flight review allows you to exercise
  the privilege of pilot in command in all categories and classes of
  aircraft on your pilot certificate.