Is only Remote Desktop.app upgraded to 3.6 or are the clients upgraded to 3.6 as well?
Assuming you upgraded the clients to 3.6 then do the following to see if the screen sharing server process is enabled to run:
1. ssh to an affected client
2. Execute: sudo launchctl list | grep screen
If the service is enabled then you will see the following output:
| - | 0 | com.apple.screensharing |
If the service is running then the next thing to check is to make sure the expected processes are running and under the correct user ids.
Execute:
1. Start a screen sharing connection to an affected client (expected of course that it won't actually connect)
2. ssh to the affected client
3. Execute: ps alxww | grep -i screen
You should see something like this:
0 64671 1 0 33 0 2572076 85544 - Ss ?? 0:05.26 /System/Library/CoreServices/RemoteManagement/screensharingd.bundle/Contents/Ma cOS/screensharingd
501 64673 238 0 33 0 2567544 23064 - S ?? 0:02.94 /System/Library/CoreServices/RemoteManagement/ScreensharingAgent.bundle/Content s/MacOS/ScreensharingAgent
This first column is the uid under which the process is running. screensharingd should be running as uid 0. ScreensharingAgent should be running as the uid of currently logged in user (501 in the example above) or 0 if no one is logged in.
If the uid for screensharingd is not 0 and/or ScreensharingAgent is not running then something may have gone wrong when the service was restarted during the client upgrade process. If possible, try rebooting the machine and see if you can control the screen after the reboot.