Change to an input that has the snowy static on the screen for a while and it'll pretty much wipe it clean.
I've had a Panasonic 50" Viera for a little over a year now in my bedroom. Sometimes when I first turn it on, before I get picture and the screen is black I'll see a logo from the night before ever so lightly lit above the black background. When the picture hits, it clears it. It's not permanent.
My parents saw mine and decided to get the exact same model for their bedroom. As far as I know, they have no issues with theirs, and they're not techy nor do they understand any of the ways to prevent issues. They probably just watch whatever just like they would have on any other TV they've owned over the years. I also think they've probably got 3-4x more hours on their TV by now... Even though I got mine first.
There's also an app in the TV for screen wiping that runs bars across to clear out issues. I just do the fuzzy channel trick now and then if I feel like it. There's nothing stuck on my screen, though.