The EPA's initial review of the commerical uses for hydrogen peroxide in concentrations lower than 10% include disinfection of cultery for food service, as it leaves no harmful residue, but I don't recall them mentioning its use for washing food. Hydrogen peroxide tends to react with a lot of organic chemicals, which is part of why it's a good disinfectant.
Also, if you do use any hydrogen peroxide at all for whatever purpose, make sure to clean up any spills promptly, and then wash the rag, napkin, mop or towel with water right away. Hrdyrogen peroxide has a significantly higher boiling point than water, and puddles of hydrogen pexoide increase slowly in concentration as a result. There's been some studies which show that even concentrations of hydrogen peroxide below 30% can cause explosions and/or fires when in contact with catalsysts, such as metals (including platinum and copper) and some textiles, including cotton, which a handy rag or mop might well be made of.