Awesome, Dear Boy: This is part of the reason why Paul Verhoeven did the film. He initially rejected the opportunity to direct it when he read the script and thought it was silly and stupid. He changed his mind when his wife convinced him that there were more layers to the story than he initially thought, and because the writers pointed out the amount of Gorn there was, to which he responded "Well, I've never seen the hero get his hand blown off!"
Casting Gag: Just before meeting with Dick Jones, Boddicker, played by Kurtwood Smith, hits on one of Jones' secretaries, who makes no effort to hide her disdain for him. Said secretary is Smith's wife!
Cast the Expert: The paramedics attempting to resuscitate Murphy after he is shot up with holes were played by an actual trauma team. They were allowed to improvise their lines, and on the DVD commentary the writers mention how it turned out better than what they ever could have thought up. One reason it worked so well is that the image of a trauma team working on a dying man in such a calm, emotionless, business-like manner feels incredibly creepy. Most people expect the ER team to act like they do on TV.
Enforced Method Acting: When Boddicker spits blood onto Sgt. Reed's desk and says "Just give me my fucking phone-call!", the actors playing the cops in the scene weren't told Kurtwood Smith was going to spit out blood. Reed reflexively backs away and says "Shit!"
Playing Against Type: Prior to playing Dick Jones, Ronny Cox played nice guys. However, Dick Jones also set up a new type for him, as proven by Senator Robert Kinsey and Vilos Cohaagen. Kurtwood Smith was also known for slightly more refined and elegant characters (while still bad guys) and not the unsophisticated thug Boddicker was.
Real-Life Relative: When Clarence Boddicker visits Dick Jones's office, he flirts momentarily with Barbara, Jones's secretary. She is played by Joan Pirkle, Kurtwood Smith's real wife.
RoboCop was supposed to stop the rapist holding his target as a shield with a precision headshot. When staging the scene, they saw how perfectly a bullet could fly through the woman's dress, so they went with that to make it more awesome than what would have otherwise happened.
The politician being thrown to the ground was supposed to be just out of sight. The dummy they used for the scene had its legs kick up comically when it landed and was visible to the cameras. It looked too funny to leave out.
Rutger Hauer of Blade Runner fame was Verhoeven's first choice for Robocop but was deemed too stocky for the suit once they realized just how big the suit would actually be - and how much bigger it would become when they had to start building it around an actual actor and stunt men. Arnold Schwarzenegger was also reportedly considered but was rejected for the same reason when they realized they would need a much thinner, leaner actor. Enter Peter Weller in his most iconic role.
Joe was originally supposed to have a much more gruesome death - in the original script during the climax he got knocked off a scaffold and was impaled on a poll when he fell, and would then be eaten alive by dogs. The finished film opted to simply have Robocop shoot him.
Paul Verhoeven wanted the death of Boddicker to be more gruesome as well - he originally wanted to have Robocop stab Boddicker in his chin and show the blade going up Boddicker's mouth, but the censors didn't like that. Verhoeven then wanted Boddicker to get stabbed in the eyeball but the censors didn't like that either, so he finally settled for having Robocop stab Boddicker in the throat (the director's cut features a more gruesome close up of this than the theatrical version).