The specific message is this: The operation can’t be completed because an unexpected error occurred (error code 100022).
When does this error occur exactly?
Personally I suggest to open the Console.app within Applications/Utilities as it often gives better information about errors.
Flash Player Install Manager: Unable to execute privileged task.
As an example
This one is obviously related to installing or updating the Adobe Flash Player
First I would try to uninstall any previous version using the Flash Player Uninstaller [Broken Link Removed]
In addition I would also do the always recommended Repair Permissions within the Disk Utility (Application/Utilities).
After that you should not encounter an error installing the latest Flash Player
I'm still not sure if and how this might be related to the above 100022 error so feel free to report back.