I just noticed something...
I am very new with Flex so please don't be annoyed...
I guess to use the IdentifyTask, I need the ArcGISTiledMapServiceLayer (IS THIS A CORRECT STATEMENT??). BUT I also need the Dynamic TOC and the Time slider (which needs both the tile and the dynamic services), so I also added a ArcGISDynamicMapServiceLayer on top of that. I think that is why it is doing like shown in the screen shot. The problem is not only that it doesn't look right, it also does not work correctly. Every time I try to click on the scrollbar (of the identify popup), it thinks I am clicking on a location of the map. I guess that is because I have another service on top of the Tile service.
Any help, please??