It maybe would have been more correct if Hera had written on a clay tablet instead of a scroll. All Minoan and Mycenaean documents that have been found are written on clay tablets or on potsherds. It is possible that they also wrote on papyrus, since it would have been available from Egypt, but if so none of those documents have survived. Anyway, a small papyrus scroll was so much easier for Athena to carry - and probably much easier for Hera to write on as well. If she would have told Zeus everything that's happened on a clay tablet, she would have needed a pretty big one.
Yeah, lightning lessons. Like driving.
Oh, did not know about Athena's ability to use the lightning - comic time, learning time :)