I've done this before, and it looks like I need to do it again. I've used plastic polish which is supposedly meant for this. I guess toothpaste
could work as well. In really bad cases people have recommend wet-sanding with 800 and finer grit before polishing.
One thing though, if doing this by hand on really bad headlights I'd recommend wearing some disposable plastic or latex gloves. Somewhere in the
process of doing my second headlight (with the fine sandpaper without gloves), my fingerprints were gone and I was bleeding ever so slightly through
pores. Didn't notice until I went for the polish after wet-sanding it...
Hurt like a (censored)! Turns out that really fine abrasives are still
I'm fine and fingerprints are back now, but some things are learnt through experience.
That's the problem with polycarbonate lenses. They're hard to keep nice after about 10 years. I've also heard that ammonia-based cleaners (that
you'd normally use on glass) are bad for them (accelerates oxidization of that particular plastic) and that you're supposed to wax them. (Too late
for my car though.)
I think it's more than just cleanliness being a factor. My tail lights are almost like new in comparison. So road grit and who knows what else does
its share of wear and tear.