What are the disadvantages (if any) of using a supercritical airfoil?
A supercritical airfoil has these characteristics:


Large leading edge radius
Comparably flat upper surface
Rounded lower surface with a maximum thickness location at around 50%
Flat or even negative camber in the forward section
High positive camber in the rear section (rear loading)


The large leading edge radius allows it to create more lift than comparable airfoils at high angle of attack. After R. Whitcomb re-invented supercritical airfoils (they had first be developed by K. A. Kawalki in Germany in 1940, and British airfoil research resulted in similar shapes, first used in the VC-10), he transferred some of their characteristics to a GA airfoil, the GA(W)-1.

From the Wikipedia article on Whitcomb:


  The unusual airfoil unexpectedly aided general aviation as well; its
  rather blunt leading edge allowed it to generate high lift
  coefficients before stalling, and Whitcomb published a low-speed
  airfoil which he called GA(W)-1; it is now routinely used in light
  aircraft and gliders.


As usual, Wikipedia is mostly correct, but the use of the GA(W)-1 on gliders is everything but routine. This gives an indication of their drawbacks:


The low forward camber limits the range of the laminar bucket to lower lift coefficients. A good glider airfoil tries to maintain the laminar bucket almost up to stall.
A positive camber throughout will produce higher maximum lift coefficients than what a supercritical airfoil is capable of. That is why the GA(W)-1 uses only the blunt nose and the rear loading, but not the camber distribution of supercritical airfoils.
The high rear loading gives them a large, negative pitch coefficient which translates into a larger travel of the center of pressure over angle of attack, requiring a larger horizontal tail. In airliners this does not matter because their large flaps dictate the size of the tail.