Welcome to Mrs. Clean!
Are the wine glasses made of crystal?
I?m assuming that regardless of the type of glass they are either pitted, which will happen to any crystal that is run through the dishwasher using automatic dishwashing detergent that contain phosphate, and/or your wine glasses have hard water stains on them which are caused from microscopic deposits of minerals such as lime, calcium or magnesium that are contained naturally in tap water.
So the bad news is that once a glass is pitted, it cannot be repaired, but hard water stains made of minerals (that can become further stained with wine) can be helped.
You can purchase a hard water remover and wipe the glasses down to remove the stains, or try a soak in plain white vinegar to remove hard water deposits
I hope that helps.