Your security settings may prevent you from downloading Skype directly from skype.com. In Mac OS X Mountain Lion, these may be set so that they only allow downloads from the Mac App Store:
To change your security settings to allow downloads from places outside of the Mac App Store:
1. In the menu bar, click the Apple icon and select System Preferences....
2. In the Personal section, click Security & Privacy.
3. Select the General tab.
4. Under Allow applications downloaded from, check Mac App Store and identified developers.