It seems that when the firewall option is enabled (apparently it’s disabled by default) you can only run Skype once without reinstalling it. The second time you try, it bounces a couple of times and stops.
A Skype forum thread about it can be found at http://forum.skype.com/index.php?showtopic=100329

From what I can gather when the firewall is enabled the first time you run Skype an alert is displayed asking if you want to enable the Skype application to have network access. When you confirm it, Leopard will sign the application so that it knows if it’s been modified and can re-prompt about network access. Unfortunately this involves modification of the Skype application which performs an integrity check on itself when it’s run. Since Leopard has modified the application, Skype refuses to start and logs in /var/log/system.log;
Oct 30 18:07:27 hostname [0x0-0x1a01a].com.skype.skype[257]: Main starting
Oct 30 18:07:27 hostname [0x0-0x1a01a].com.skype.skype[257]: Check 1 failed. Can’t run Skype
The workarounds are one of the following:
1. Reinstall Skype from the .dmg every time you want to run Skype
2. Select Skype.app, right-click on it and choose Get Info from the menu. Tick the box that says Locked. A small padlock will appear on the icon.
3. Turn off the firewall.
Neither of these are very good as the first is just a pain in the neck, and the second results in being asked for confirmation that you wanted to run the file that was downloaded from the internet, and then being asked for confirmation that you want to allow it to have network access. The third, well.. if you’re anywhere other than at home behind a NAT router, it has the possibility of leaving your Mac open to attack.
I opted for option 2 but it’s quite awkward and I’ll be glad when an upgrade is released.