@Husar and others: you can check for a dead pixel, rather than dirt, using a tool such as this

Run the time cycle, and carefully check the screen for any place where it is not an absolutely uniform colour.

If, for example, you've got black dots on the green colour slide, you've got a dead pixel

I'd say get it replaced if at all possible; and if you do, ask to see the monitor in the shop, and run such a program on it. No need to make the round trip multiple times