fixing up headlights

You need to work up in a progressive fashion. Try the toothpaste, if that doesn't get you the results you want, then go to an automotive polish. If that doesn't help, you may need to use a compound (like Meguiar's 105, for example). If that doesn't work, then you might have to sand. As you go more agressive, you may have to work backwards again (going finer and finer) to get back to the clear finish you want.

As I said before, they don't look bad in your picture, I'd stay with mild methods, particularly since this isn't your car.
 
This is on my cousins Ford Focus with some Megs UC and a cutting pad by hand. Yours looks to be in much better shape than what those lights did.
 
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