I have no clue how well it works, but WikiHow explains a couple possible ways to fix a stuck pixel on an LCD monitor. I have heard about the video of quickly flashing colors fixing things for some people. But this site suggests something else for when that doesn’t work, you lightly massage the area of the screen with the dead pixel. This blog post adds some confirmation that these methods can work and suggests you might try combining them. Massaging my LCD is not something I would like to do, but if the pixel was annoying enough I guess I would give it a try as a last resort. Luckily so far I don’t have any that I know about.