As Slyowl already mentioned, yes it leaves some tiny scratches because it removes the painting in a different way. I will not recommend it for removing prints from glass or transparent bricks.
I have only use tooth paste on minifig torsos and when the print has been removed I have always placed a decal on the surface afterwards. For that propose the tooth paste works great.
I have tried with nail polish remover but I won't recommend that (at least not the one I used), it almost removed the whole torso, speaking of strong chemicals! And girls use this on their nails, crazy!
Unfortunately I have not had the chance to try with brasso yet so I can't compare it to that.