I´m having a lot of 404 errors on all my wordpress sites hosted

I´m having a lot of 404 errors on all my wordpress sites hosted at Hostgator.
In webmaster tools from google I can´t get any information.
I have installed a plugin 404 to 303 to redirect all 404 errors to a existing page.
Each day I get aprox 300-400 errors. I´m very concer with it, I guess this is symptomatic of a larger problem whose origin can be someone with bad intentions who want to exploit our limited experience in post wordpress websites.