Actually the PSP is pretty well-known for having dead pixels. Just google for "dead pixels". I don't really like the term though, because many companies nowadays try to push the definition of "dead" as "dark-only" rather than both bright and dark (with bright ones being called "stuck pixels" instead), so they can handily say "those are stuck, not dead, and they don't count in our dead pixel policy" when it's the bright ones that are annoying. I prefer "sub-pixel defects" since that's what they really are (they happen on a sub-pixel basis) and companies can't weasel around with the term. Oh well.
Some dead pixels can be fixed by rubbing the area. I'd recommend putting a piece of paper over it before you try though (your fingertip is sufficient), so that you don't rub off whatever protective coating the LCD has. Or um yeah a microfiber cloth. A screwdriver is recommended only if your screen's protective coating is made of metal.