Hi Ingeborg,
My knowledge in the area of JavaScript and HTML isn't going to be sufficient to tell you how to do what you're asking, but I believe that the stream layer object in the HTML should have the information necessary to allow the "identification" of features. That is, you should be able to add code which will allow users to retrieve attributes associated with an event such as the event's date/time by clicking on a feature's location. I say that because part of the edits you can make to the HTML within the <script> tag as a developer includes a variable declaration for the layer (var layerDefinition = ...) which includes attribute fields.
If you look in the attached Twitter.zip archive you'll find a TwitterStreamLayer.html which was updated for the revised Twitter tutorial. (This tutorial should be up on the product gallery soon...)
Look for the first block of code below the layerDefinition declaration. You should see code which identifies the basemap, the map's center, and zoom level, then code which invokes a setClickEvents() function to establish callbacks for click events on the HTML form's two buttons. I'm assuming that with a sufficient knowledge of JavaScript you could establish a callback for a mouse click or double-click overtop the basemap which would find the nearest feature within a tolerance and report back to the user the attributes of that feature in some sort of pop-up. I just don't know how do actually do that.
Hope this helps -
RJ