Hydrogen peroxide is generally used as an additive to your waterings after you've done a flush. It disinfects the soil and actually helps the plant because as its killing bacteria and producing little bubbles of oxygen and giving your poor drowned roots exactly what they need.

Ive never heard of it as a bug killer though. If your afraid of spider mites man really just get some neem oil, its not that expensive and after all the reading I've done on the subject (I'm currently battling an spider mite infestation, keeping them under control with a gentle vacuum every few days, stinky suggested it in a thread. As well as hitting problem areas with an anti mite spray.) Once i get my neem oil (grabbed some off eBay) and give it a test run ill be more'n happy to share my results with you.