Some of the disadvantages of the CVT transmission include that it has a limited ratio range and that it is very costly. It also does not have the capacity to cope with big engines or high torque loads. The CVT transmission has less reliability compared to automatic transmission. Check out http://www.cvt.co.nz/cvt_advantages_and_disadvantages.htm.
My Saturn Vue had one and the only disadvantage I knew of was that its a sealed system. Meaning you can't check fluid levels, no dipstick, and if something went wrong you had to replace the whole system instead of doing a rebuild or replacing whatever component failed.