Can hydrogen peroxide break down or damage cavity fillings or dental cement?

No damage: You are asking about hydrogen peroxide 2% solution over the counter i would assume. I tell my patients who have some form of gingivitis to rinse with it diluted 50% water 50% peroxide. It iis ment to be used as an antimicrobial disinfectant. I have not noticed any negative effects on restorations.

No.: Hydrogen peroxide has not been shown to cause any damage to fillings, or dental cement. It has, however, when used as a mouth rinse, been linked to tissue damage and pre-cancerous changes in the epithelium. I would urge you not to use hydrogen peroxide as a mouth rinse. Proper brushing and flossing will clean your teeth without the use of any rinse.