Hi Dan,
The easiest way to reproduce the Kanban bug is with this procedure:
1. Create a new task list.
2. Add three tasks: Task 1, Task 2, and Task 3.
3. Make Task 2 and Task 3 subtasks of Task 1. (Indent them both by one level.)
4. Switch to the Kanban view and ensure that Options→Show parent tasks is selected.
5. Move Task 3 from "Not Started" to "Completed."
You should get something like this:

I would expect that parent task Task 1 would be shown in "Completed" just as it is in "Not Started," since both Task 3 and Task 2 are subtasks of Task 1.
It could be argued that until both Task 2 and Task 3 are finished, Task 1 is still in progress (and therefore belongs under "Active") and should not appear in "Completed." But if that's true, then "Task 1" shouldn't appear in "Not Started," since Task 3's completion implies that Task 1 has been started.
Also, I agree that Task 1 is not completed when only Task 3 has been completed. But the problem is that Task 3 does not show its parent task, even though Options→Show parent task is selected.
If Task 1 not being fully completed is the reason that Task 1 does not appear in "Completed" as the parent task of Task 3, I suggest that an alternative visual way of showing the parent task be implemented. Perhaps you could draw an arrow from Task 3 in "Completed" that points to Task 1 in "Not Started," or you could add "Task 1" to "Completed" but somehow show that it's only partially completed.
As it is now, "Task 3" is in the "Completed" silo without giving any indication of what its parent task is, despite the fact that Options→Show parent task is set.
Thanks,
Steve