Following an update to Mountain Lion on my client machine where I have Apple's Remote Desktop running, attempts to control other remote machines still running Lion fail with "authentication failed" errors. The passwords I have for the remote machines are correct, and I can ssh to those machines without issues.
What do I need to do to get Remote Desktop working again? Ideally, this should be something I can do from within Remote Desktop or ssh, as physical access to the remote machines is difficult.