In the Advisors section of the app, the Weekly Nightfall Strike and the Daily do not show any indication that they have been completed. The VoG Raid and the Weekly Heroic do show how much of them has been completed, but there's no way to tell by looking at this screen, whether or not that character has completed said mission...
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Because you can easily see if you completed them on the destination screen, so it really is unnecessary for the app.