If you purchased FaceTime from the Mac App Store, the first thing that I would recommend is removing and reinstalling the application. Take a look at the articles below for more information.
If you continue experiencing issues, you may want to review the article below for some further troubleshooting instruction.
Hope that helps,
Sorry. Your proferred solutions did not help. Facetime came with Lion update,so it was not purchased through the App Store.[ BTW their recent Factime is 1.0.1 (2011!) mine is 1.1.1 (9/26/12).] So, downloadng past purchases i N/A.
Been there, doubled checked those things.
Additionally- Facetime works well on my iPdad and iPhone4s.