Previous closed post said it wasn't possible to hide completed Tasks in Outlook Today View with Outlook 2003.
Actually the Tasks that are completed that still show up in Outlook Today are usually ones that do not have a completed date in the Task. I.E. It will show a NONE for the completed date.
I'm not sure what causes the NONE to appear, but if you go to the Task View of Outlook use a view that displays the Completed Date and sort by that column you can enter a Completed Date on those Tasks (prior to the current date) and the completed Tasks will no longer display in the Outlook Today view.
Actually the Tasks that are completed that still show up in Outlook Today are usually ones that do not have a completed date in the Task. I.E. It will show a NONE for the completed date.
I'm not sure what causes the NONE to appear, but if you go to the Task View of Outlook use a view that displays the Completed Date and sort by that column you can enter a Completed Date on those Tasks (prior to the current date) and the completed Tasks will no longer display in the Outlook Today view.