Neither brushing your teeth, nor rinsing with mouthwash removes bacteria-rich "biofilm" from between your teeth. The only effective way to clean between your teeth is to floss properly every day.
By some accounts, 80% of tooth decay begins in the pits and fissures of teeth. Toothbrush bristles may not be able to completely remove food from those areas. Dental sealants and fissurotomy techniques may help protect against these types of cavities.
Nearly three fourths of adults have some degree of periodontal disease. Aside from the traditionally discussed dental complications of gum recession, tooth root decay, tooth loss, bite collapse and bad breath, there are now well documented medical complications of periodontal disease, such as heart disease, stroke, diabetes, and peripheral vascular disease.