The questions were posted to mark World IP Day 2014, which had the movies as its theme. Below are the answers, with links to the relevant pages on the Internet Movie Database.
1. In The Third Man, Harry Lime steals, dilutes and resells which drug? Penicillin
2. Which actor played the role of a patent attorney in the US TV series Harry's Law? Kathy Bates
3. Which 2010 Hollywood movie is about an IP ownership dispute? The Social Network
4. The characters Wallace and Gromit have been used by the UK IPO to promote innovation. What is the name of the feature film in which they appear? The Curse of the Were-Rabbit
5. Which 2006 thriller about an inventor trying to protect his innovations from becoming casualties of the Cold War was originally titled Intellectual Property? Dark Mind
6. Which Eddie Murphy movie involves a burger chain infringing McDonald's trade marks, including using "golden arcs" and the "Big Mick"? Coming to America
7. David Bowie uses technology from another planet to patent many inventions on Earth and accumulate a fortune in which film? The Man Who Fell to Earth
8. In which 1998 disaster movie do Billy Bob Thornton and Ronald Quincy briefly discuss whether patents apply to outer space? Armageddon
9. In which 1951 movie does Alec Guinness portray an inventor who is relentlessly pursued by management and trade unions to sign away the rights to his invention of a suit that never needs to be cleaned? The Man in the White Suit
10. Which movie features Gwyneth Paltrow claiming Stark Industries has "the best patent lawyers in the country" while making accusations of "illegal seizure of trade marked property"? Iron Man 2
11. Which movie features the line "We hold patents on a few gadgets we confiscated from the visitors. Velcro, microwave ovens, liposuction"? Men in Black
12. The movie Flash of Genius dramatises the battle between a single inventor and a large American car company over a patent covering which invention? Intermittent windshield wipers
13. In 2009, Nicolas Cage played an MIT professor who predicts catastrophic events by decoding numbers gleaned from divine sources. A patent holder sued the studio behind the movie, claiming that the decoding method portrayed infringed its patent. What is the name of the movie? Knowing
14. Which 2012 movie is about a Chinese-American IP lawyer who is transferred to China? Shanghai Calling
15. Which two movie megastars appeared in a 2005 anti-piracy awareness advertisement? Arnold Schwarzenegger and Jackie Chan (watch the ad on YouTube)
Congratulations to everyone who sent in correct answers by email and on twitter and particularly to Janice Denoncourt of Nottingham Trent University, who answered all the questions online.
The only remaining question is: how many of these movies have you seen?