Off the top of my head

*Aamir Khan never stands still in the entire movie. He is always swaying in some direction. Apparently, he concluded that the our generation never stand still after observing his nephew. (Making of 3 Idiots)

*The idea of the flying helicopter was offered by Dia Mirza (In an interview by Vidhu Vinod Chopra)

*Aamir Khan makes a statement in the movie that people in India first study engineering, then management, and finally become bankers. If you wanted to be a banker all along, why study engineering?
This is exactly the career path Chetan Bhagat chose ( the guy who wrote the book from which this movie was inspired). This may or may not have been a reference to him. (conjecture)

* Shahrukh Khan was the offered the role of Rancho. He refused citing date issues.

* Various technologies shown towards the end of the movie are real world inventions.( When Farhan and Raju reach Rancho’s school in Kashmir)

* The Chinese were interested in remaking the movie.

*Imperial College of Engineering as shown in the movie is based on IITs