According to a user report, it seems that new Macbook Air is having some issues with Skype 2.8.x. If you’re using Skype 2.8.x for Mac OS X on Macbook Air, there’s a good chance that you won’t be able to use Skype at all, because Skype gets stuck during the login.
Many users have complained about this, but it seems that there’s no official solution from Apple or Skype at the moment. Only solution that is available is switching to the earlier version of Skype, at least to the Skype version 126.96.36.1990. On the other hand, if you’re using Windows 7 and Skype on the Macbook Air, there’s no problems.
This is an annoying bug, and so far, only solution is to switch to the previous version of Skype, but we’re hoping for official solution soon enough.