Every time I restarted Skype it promised a new release of 6.0 that it would download but then fail to update:
Skype was unable to install the update because the old application can’t be overwritten.
Pretty unhelpful error message.
It was an ownership problem: I finally found the solution today in this thread in the Skype forum:
1. Open terminal
2. sudo bash
3. ls -l /Applications
check which non root owns most apps (third column)
4. ls -ld /Applications/Skype.app/
check which user owns the Skype app
5. If Skype.app is not owned by the usual user then
chown -R whateveruser /Applications/Skype.app/