It seems from the original description of the event, it slid off your bed and onto the floor, after which you noticed the "dust" in the display. This might seem to indicate, as some have already mentioned, that this piece of debris was already somehow in the display and perhaps had managed to lodge itself along the inside edge, unnoticed. The shock, however minor, might have dislodged it into a more prominent view.
As tveger suggests, blowing into the earphone jack or along side the menu buttons, or perhaps some pressurized air, could dislodge the culprit. My friend also suggested trying a magnet, although not sure how that would affect the display. Also rubbing the display with your finger might generate a small electromagnetic field and cause the particle to move, providing that it is not a pixel issue.
I am aware how disconcerting these issues can be when they affect the display, after all, it's literally staring you in the face. Sometimes we have to live with these minor issues, like the "ding" in the car I mentioned above. You could also send it back to Uniden--- I forgot if you mentioned whether or not it is under warranty, or just continue to use the radio as-is and tolerate the imperfection; many a great guru will tell you that nothing in life is perfect. That's likely what I would do--- continue to use it an enjoy it, and if something more substantial occurs in the future you could then send it back to Uniden.
In fact, if there is a bright side, once a unit starts to get a little "weather-worn", some of us actually tend to use it more, and bring it out more, and carry it more, since it's already a little "scuffed".
I understand and empathize--- I remember when I was younger these things would sometimes drive me crazy. In the scheme of things, it's just a minor issue and it marks that radio as uniquely being yours.