>If I do this on my local machine - even selecting my own account - it prompts me for username and password when I exit the New Task Dialog.
>If you're using a SYSTEM account, then there should be no password prompt at all.

Correct, if you create a new task, at Save time, it will ask you for the password. But, if it is already there, and we change the password on the domain controller, and we have to adjust the task for the credentials in regards to that account password change, there is just no way to click somewhere to adjust the password. As the account is already the good account to use, so far, the only thing I have found, is to remove the account, use a temporary one, add the password of that temporary account, save, go back to edit the task and switch back to the good account which will then ask for the password when saving.

...unless there is a better way to do it, which I would very much like as this is a procedure we have to go through on Monday night and because we have to double up on everything, this will require 100 password changes instead of 50.