Gentlemen,
I've been visiting your forum since many years, but never tried to join it. Today I decided to change the status quo in the hope I have a few more details to add.
There is a very comprehensive article in Warbirds International, Vol.27/No.4 (Maj/June 2008) about the Mitchells used during the filming of "Catch 22". One of the photos published shows IMHO the same nose section as the one questioned.

The photo copied from the magazine was made during the filming of the bombing raid over the sea with Alan Arkin as Yossarian in the bombardier’s compartment, thus the "Dumbo" nose art.
Below are 2 screenshots from my DVD-copy of the movie, showing the same nose section with closed and opened bomb bay doors.


I think
this is not the same nose section as in the photos from the Tennessee museum shown in previous posts, nor is it the one mentioned
here and
here.
As you see the nose section has no top turret, but "football" antenna on the underside of fuselage, the engines (fake or real) have the wide scoops for the Holley carburetors and all Clayton stacks are there. There is no navigator's window too. I think the nose has no real glazing (probably for the filming purposes), but some transparent plastic foil or similar material. There is a visible center frame for the front roof window (as stated in a post earlier).
The real "Dumbo" in the movie is a different a/c - see another screenshot below:

Note the high airscoops fot the Bendix carburetors and the second opening for a nose gun in the bombardiers section. The roof window is one piece with no center frame. Based on several sources "Dumbo" has the original s/n 44-30493, registration N9451Z and was coded
6V in the movie. BTW this was one of the few odd "movie mods" with the dorsal turret mounted behind the wing.