I also had a black dot on the screen of my first Droid! When I went to buy my Droid, the default background was dark grey so i didn't notice it but after i went home to play with some of the features, I changed the wallpaper to a white one and noticed that there was a very small black dot towards the upper part of the screen. At first I thought that it was dirt or something so I tried to wipe it off with a cloth but it wouldn't come off.
I went to the Verizon store the next day to see if the workers could get the dot off. They were very careless with my phone and rubbed their shirts on it, rubbed it on the counter, used an antibacterial wipe and swiped it around the screen but it wouldn't come off. The next thing that I am asked is if the dot is a "big deal" to me and if it was worth me having it exchanged. I told them that yes, it was a big deal since I paid $200+ for a brand new phone and I didn't want a defect. Then they exchanged my phone for another new Droid and I haven't had any problems ever since
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