二重敬語 is presumably considered bad style (or simply incorrect).
I hear/read 拝見いたしました all the time. Is it an example of 二重敬語?
I understood 二重敬語 to be a little more complex than "used a polite form more than once in a phrase".
To be a bit more precise, I think that to express a verb in 敬語, one should make the verb polite, but only once, so that
is 敬語, but
拝見いたす might be fine, because 拝見 is a (敬語) noun and いたす is a (敬語) verb; or it might be a problem, because 拝見する is a (敬語) form of 見る.