The 4 o'clock / 8 o'clock lights usually show up whenever footage from WNMHGB is used, but they are only lights, and an easy problem to deal with. I just thought I'd mention them for completeness.
Good speculation about the "bridge" dome! The transparent section as seemingly presented in The Menagerie
and The Cage
never made a lot of sense except as a a SFX POV shot (of either the audience or the Talosians). Or that would be one large, fragile ceiling!!! The job of the infamous zoom-in shot is to provide a sense of scale, which is does quite well.
In any case, we see the ceiling of the bridge when Kirk walks in during WNMHGB, and it is definitely opaque:
(middle upper picture)