Right click the downloaded TweetDeck installer file (.air file) and select 'Open With'
Browse through: Program Files/Common Files/Adobe Air/Versions/1.0/
Select the 'Adobe AIR Application Installer'
TweetDeck should now install correctly.
Mac OS Fix
There may be untrusted or self-signed certificates in the Keychain - This has been found by other users to cause problems with the install. It is advised to remove any self-signed certificates in order to not have this AIR file problem.