I had a scratch on my 27" Mac monitor. It is a glass screen and unfortunately the scratch was right in the middle and very distracting.
I too was very leery about putting toothpaste on my precious screen, but after googling around I was not getting any better answers so I decided to give it a try.
I took a little bit of toothpaste. It was not the "simple" kind of toothpaste mentioned above but one of the ones with all the other stuff added. I suspect the kind of toothpaste does not matter.
I used a piece of white computer paper to rub the toothpaste on the scratch. One YouTube video that I saw said paper worked better than tissue so I went with that. And the verdict? It works! If I look very closely I can still see the scratch but it is way better now.
It took me about of 5-10 minutes of rubbing. I went pretty slow because I was paranoid that I was going to screw up my screen, but there do not seem to be any ill effects.
I strongly recommend you give this a try. Note that this will only work with glass screens.