Stuck pixels are usually caused by manufacturing defects, and they will often stay illuminated for the life of the panel. In many cases it's possible to fix the pixel using either software tools or manual manipulation.
The software solution will generally flash a series of images that vary in colour and intensity onto the screen in an effort to unstick the pixel.
Manual manipulation involves gently pressing on the affected area with something like a pencil eraser. Doing this compresses the layers of the panel, forcing the oil within the panel to move.
Be careful, though: this is by no means guaranteed to work, and it could create even more stuck pixels or move the problem to elsewhere on the screen rather than repairing it.
Dead pixels and hot pixels are generally the result of faults in the circuitry of the panel. It's usually the case here that the transistor does not switch states properly.
Dead pixels generally mean that the transistor has failed completely, and this is rarely fixable.
Hot pixels may be due to manufacturing defects. They can often be fixed in the same way as stuck pixels, but again, success is not guaranteed.
More help
If you have stuck or dead pixels, we recommend that you try a software solution and only press on the screen as a last resort, as you could end up damaging the panel further. UDPixel is a program that tries to find and fix faulty pixels, as does JScreenFix.
If your screen is new and seems to have an excessive number of faulty pixels for its class, you should contact the manufacturer for a replacement instead.