Dead/Stuck pixel-like object seen when computer is off

I'd guess you have something stuck between the glass and the LCD.

 

^ yeah. I don't think you can see pixels when screens off without some 3rd party tool

 

This is more likely a small piece of white dust/dirt. It's not possible for a pixel to be illuminated a stuck color when it isn't powered last I checked.

 

It may be annoying, but I'd probably just deal with it. You'd basically need to remove the glass from your display(I'm assuming you have a unibody MacBook (Pro), otherwise you wouldn't have glass in front of the LCD). If you were to do this, you run the risk of introducing another piece of debris.

 

You could always take it into an Apple store and see what they say. I don't think they're going to charge you just to look at the computer.

 

If it's out of warranty it's quite unlikely Apple will do anything. The glass panel will need to be removed and the inside cleaned. If you attempt this, in the process, there's a decent chance that a second spec of dust will sneak in there and cause the same issue elsewhere on the display. If I were you, I'd deal with it until your next upgrade. If it's only a problem with the computer off, don't worry about it.