Yes. Final Draft v.8.0.3.1 has been engineered to be compatible with Mac OS X 10.8 (Mountain Lion). If you have Final Draft 8.0.0 through 8.0.3, you can download the free 8.0.3.1 installer HERE.
Final Draft v.7 / 6 / 5 are not compatible with Mountain Lion.
If you own Final Draft v.7 / 6 / 5 and you want to run Final Draft on a Mountain Lion computer, you will need to upgrade to v.8. This upgrade is not free. Click HERE for more information on purchasing the v.8 upgrade.