Seems like serious engineering only appears in comedy form:
There are parts of "The Brothers Grimm" 2005 that show the mechanical engineering of the time?
"Deal of the Century" with Chevy Chase, Sigourney Weaver & Gregory Hines has a part where a piloted plane competes with a UAV which foreshadows today's military.
Being Scottish, I have to say the Flying Scotsman; a true story about Greame Obree, a cyclist who built his own cycle and beat the world one hour record as well as other titles http://www.imdb.com/title/tt0472268/
I knew Greame at school and his real life story is incredible http://en.wikipedia.org/wiki/Graeme_Obree
The Hunt for Red October was good - so was crimson tide. Of course the movies 2001 and 2010 - they were science fiction however... many of the predictions have come true and some are funny like Pan-am airlines featured in 2001 or the bell labs video phone. Many engineering marvels we have exceeded today and some we are painfully behind in like todays space program is a shadow of what it was in the US at that time.
Hmm I don't remember a "Flight of the Phoenix" movie from 1965 where James Stewart did any engineering, but there was one with James Stewart where Hardy Kruger did some engineering on converting a twin engine plane to a single engine one.