After selecting one or more Tags to filter discussions, the only way to see what tags have been applied is to click on Filters. (The TagID does show in the browser URL field, but that is not descriptive.) The applied tags should be highlighted in the tags 'cloud' to make it readily apparent which tags have been filtered to.
[EDIT: I discovered after posting this that clicking on Filters only shows certain tags from a predefined list, not the full set shown in the tag 'cloud'.]