Hey Dominique,
You had mentioned using ObjectID, what did you mean by that exactly?
The problem with my code, apparently, is that I'm adding a feature to the Graphics collection of my layer, but since my layer is OnDemand, whenever I zoom to the region that contains the feature that I added, it seems to be duplicating that feature on top of it, so the selected graphic is hidden.
I might be understanding it incorrectly too. This does seem to be happening only if I do this in the Initialized event handler of my layer... If I do this moments after the event has finished, this doesn't happen. I'm able to see my selected graphics.