There are several possible reasons why you may be having problems downloading Skype for Mac OS X.
You may receive a message prompting you to allow Skype to access information stored in your keychain. Simply click Always Allow and start downloading Skype for Mac OS X.
Your security settings may also 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.