Uh, just where are those wings supposed to go without intruding deep into the interior compartment and messing up what little usable space there is there?
Perhaps they just deflate? Or is that too high-tech for this chariot of fire?
Another possibility is that they roll in along the sides of the hull like a garage door. Rigidity in extended position could be achieved by a variety of means, although inflation with a fluid might be a fun and pseudo-1930s way to go.
Making the raygun telescope would certainly be practical and sort of trivial, and would help reconcile the footage discrepancies.
I really adore this little pup - and I sort of wonder if the utterly uselessly positioned windows aren't a conscious choice, here, and in other onscreen scifi (c.f. the TOS shuttle), to make sure that nothing compromising will ever be glimpsed through them...