I recently ran into a problem where I needed to uninstall WSUS and start over again. While attempting to uninstall WSUS I received a notice that the uninstall did not complete successfully, and a check of the event logs revealed the rather cryptic error 1603.
A bit of Googling turned up the following post: http://davidvielmetter.com/tricks/wsus-wont-uninstall-or-re-install/ by David Vielmetter.
The long and short of it is to open RegEdit, go to HKLM\Software\Microsoft\Update Services\Server\Setup and ensure that the two keys wYukonInstalled and SqlInstanceIsRemote are both set to zero.
After that you should be good to go, and the uninstall should complete successfully.