TFTs have an allowable "dead-pixel" number in their specifications.
At least one of the HP monitors accords with the ISO guidelines click here (ignore the fact that it says Ilyama - it's the ISO standard that's important).
Look up the specificatopns for your monitor on the HP web site. Check that it adheres to this specification document. Act accordingly.
Even if it meets the specifications, you can still try returning it and asking for one that's better. But if pixels fail in the guarantee period, as long as the specification is still met, it's unlikely you'll get it replaced under warranty. So act quickly if you want to try a return to the store.