You can try, but you'll most likely not win. In fact, Apple probably won't even take you seriously, nor will the judge. Apple has some of the world's best lawyers working for them, and I doubt that you can would wanna spend that much money hiring a lawyer, then spending weeks, if not months, waiting for anything to even happen. Chances are, Apple will win this case only because you have no hard evidence of any of this stuff ever happening. You can't just go to court and say 'oh, I went online and a bunch of people there said that they had screen issues, even after getting their screen/computer replaced.'
It's not real evidence, and I'm not sure if this case would even get attention from the media.
So, if you really want Apple to fix this issue, you need to find a way to make it go mainsteam. In other words, make it a big deal, and put it in the news and on TV. If this issue is global, Apple will have no other choice but to fix it.