CLB: I have no problem with the dome itself being transparent, I just don't think it should act as a window over the bridge. After all, this is a sensor dome, right? Where is all the sensor equipment supposed to go?
I forgot to mention, there is another shot of the bridge "ceiling":
OK, so it's not exactly a ceiling - You can see from the pattern of shadows that in both ITITNB and WNMHGB it seems they just hung vertical flats on top of the existing bridge wedges to enable the director to film his desired shot. Was it (on low resolution TVs) meant to represent a curved dome ceiling? Possibly. But if not, the ceiling would have to be even higher, at least 14' off the deck level!
One final thought. If the dome were truly a window, then it might appear black from the inside, as CLB described. Except that in the Trek universe (even TOS) this never happens - every time they look out of a window from a fully lit room, loads of stars are visible! Must be that futuristic Transparency they use...