Currently, if you click Done on a task on Home in either the left or right panes, the tasks is removed from the left pane but stays in the right pane until you either click on another task or refresh the browser.
If you click Done from within the task itself, when you come back to Home the task is removed from the left pane, but requires a new task to be selected before it is removed from the right pane. No amount of refreshing will remove it from the right pane.
We would like tasks to be removed from the right pane as well when they are marked Done.
I flagged this as potentially confusing during the Beta period. From one of my users: I’ve started to post updates and log time to other tasks multiple times this week only to realize I was still in the window for the task I just completed.