Our mare tends to grind her bit quite often. It is a hiddeous noise (like nails on a chalkboard). She doesn't seem aggitated, tense, or uncomfortable, but every couple of minutes you can hear the grinding noise. She also really tends to lean into bit contact (not in a good way) - I don't know if the two things are connected. I have been doing exercises that have worked with my other horses to soften to the bit, and learn to carry themselves rather than leaning against the bit, but she continues to lean on and even push on the bit.
The vet gave her a quick once over in with her teeth in the springs, but was not thorough at all. She is not dropping food or having any problems keeping weight. Now that I am aware of the bit grinding, I will have her teeth looked at much more closely when the vet comes out (we have no equine dentists).
I have recently ridden her in a two jointed sweet iron snaffle with copper play rings, and a single jointed sweet iron snaffle with copper inlay. She grinds in both.