Most of the time the bright pixel defects on computer monitors will not go away. However, on some monitors the pixel problems will only appear noticable when you first turn on your computer / monitor.
I actually a have a Dell Monitor that has two bright "dead" pixel lines going down the entire monitor, and will show up every time the monitor starts, however after a few minutes the bright pixels disappear and the monitor screen looks like it works correctly.
Every monitor is different, but if you do start experiencing problems and your monitor is still under warranty than be sure to get it replaced, because more than likely the problem will eventually just get worse.