Actually a dead pixel is a black pixel, if the pixel is stuck on any other colour than black it is infact a stuck pixel and is caused by a malfunctioning layer of the LCD.
Believe it or not it is possible to fix these on your own, although I think it may be a lot tricker on the iPod.
When I had a stuck pixel on my Nintendo DS, I was first advised to play a fact paced game, so that all the pixels would change colour constantly which would hopefully unstick the pixel. I believe this is something TV repair shops do, except they have a special DVD which is basically a constantly changing screen of all the colours of the rainbow, and they leave this on overnight. If you could find one of these types of videos and put it on your iPod you may be able to fix the problem.
However, this didn't work on my DS. The way I fixed my dodgy DS pixels was to turn off the DS and rub on the affected screen area with a cloth with a reasonable amount of pressure. I did this for about two minutes (note that this was after playing a fast game, this may have helped), then turned it back on and the problem was solved
. But this might be difficult on the iPod due to the glass screen :-(
You might want to google for 'fixing stuck pixels' or something to that affect, it will help you more than I can