Of course it is NOT illegal to use portable video equipment in an aircraft.
If it was permanently mounted that is something else, in terms of paperwork.
Powering it from say the cigar lighter is OK too. If the aircraft electrical system was modified to bring out power sockets to plug things into, that needs a signoff, and perhaps a load analysis.
People make such simple things so complicated.
What I wonder is whether anybody has yet mounted a camera externally, by attaching it internally (e.g. with suction cups to the internal surface of the window) and having it poking out through the little opening window which many planes have. That would avoid the usual cockpit reflections and would be a simple solution to both the practical and the legal issues.
BTW, large chunks of this thread seem to have gone missing.