Tucker: The man and his dream (1988) is an ezcellent movie. It shows how a man and his team's ingenuity can bring about great things. Unfortunately, it also shows how, in some industries, it takes more than just building a better mousetrap to succeed.
For a comedy try the 1984 "Best Defense" with Eddie Murphy and Dudly Moore about a lazy engineer in teh defense industry who bumbles around and finally gets something right.
I would submit several SciFi movies but that's easy. As a Technician, I've always like Gene Hackman's tech roles like The Conversation and Enemy of the State.
Yes, I checked out The Dish from the library a few years ago -- good movie and good tech. As a resident of Huntsville (AL), space movies like Apollo 13 and Rocket Boys are popular here. Hackers, WarGames, and Sneakers for the computer tech.
One of the best little movies you've never seen: The Dish. Based on real events, it tells the story of a small Australian village and its satellite dish that NASA wants to use as a backup transmitter for the Apollo 11 moon mission.
When a change flight schedule puts the primary dish out of range, Aussies must use all of their engineering knowledge to ensure that the history-making mission is broadcast to the world.
I'm surprised nobody has mentioned "Flash of Genius" - a film based on the true story of college professor and part-time inventor Robert Kearns' (Greg Kinnear) long battle with the US automobile industry over his design of a windshield wiper motor controller.
Iron Man - I love watching the scenes where Tony Stark is going through several iterations before he makes something work, something the second movie lacked. Inventions don't work perfectly the first time.