Code does require a dedicated microwave circuit ...but ONLY if the micro in question as part of an 'over the range and exhaust hood' install. Event there, the requirement is an indirect one ... the dedicated circuit is called for IF the hood is cord & plug connected, only because a micro MIGHT be added later.

It is quite possible that the inspector got confused on this point - dang them code seminars! [Linked Image] In general, a micro can be plugged into any receptacle - even the countertop general purpose ones- and I suspect the stove igniter can come off them as well.

Now, as to the igniter tripping the GFI, I simply don't know if that's a concern.