Land of the Pharaohs is a movie that Howard Hawks did to show large numbers of men at work - the original idea was about building an airstrip in China during WWII. The final project - set in Ancient Egypt - is a pleasant movie about building pyramids and the traps inside them. Closing sequence is impressive.
The Wages of Fear (Le Salaire de la Peur) - Not a lot of pure engineering, but plenty of technical problem-solving, as four men try to get two trucks of nitro through the mountains of S. America.
10 Commandments - Not typically seen as an engineering movie, but the scenes of Moses building the city feature some solid scenes of old-school engineeering, particularly the obelisk scene.
The Great Escape - some engineering, but more at a systems level - putting together all the parts of the escape, and dealing with managing the people who have to solve the problems.
Most caper films share this element with The Great Escape.
A Bug's Life deals with a geek trying to solve a problem and pitch it to management, The sequence in which the plan is pitched, in succession, to the initial team, the leadership of the ant colony, and the the populace thereof, is a particularly well-turned sequence.
The Wages of Fear came to mind too, dealing with overcoming obstacles. The Great Escape fits, and A Bug's Life same idea of control overcoming chaos. Bad outcomes can be seen in some of Crichton’s novels like The Andromeda Strain, The Great Train Robbery (clockwork precision) and Jurassic Park of course. Park is a classic for showing improv's ability to deal with faults & breakdowns. Airframe 1996 is also a very gripping book about the complexity of technology and overreliance on it. Phoenix is a terrific story especially since uses the human element so well compared to most recent techno thrillers. The latter flatten the characters to play up the FX razz. Film people like that since means less set time, collect pay, and on to next quickie. Just saw Abandon Ship 1957 and it's haunting me. Set on the open sea (like the desert in that way) and who is critical to survival & who's not & who decides. For now I'm leaving the life and death genre aside for a while!
There was a quite good, "made-for-tv" movie, "The Flight of the Birdmen", early 1970's. I've never seen it again, but when I looked for mention of it on imdb.com, others remembered it fondly as well. I believe that it was directly inspired by "Flight of the Phoenix", which would have come out 6-7 years early. I wish the movie would be released on DVD!
Plane crashes in the jungle, and the survivors have to get it fixed and clear a runway, before they can leave. Can't say too much more than this without resorting to a ton of spoiler tags, but it's a great movie. They did a remake some years later, which was good, but not as good as the original.
How sad, that you were not born in my time, nor I, in yours.
In The African Queen Charlie Alhnut had to build a forge in order to replace the broken propeller so they could continue their journey down the river. Later on in the film he designed and built a couple of torpedoes so they could ram them into the Louisa and sink her.
Most incredible engineering feat in this movie was anchoring the winch on top a pallet and pulling 10x its weight without moving. Love the movie though.