Plot hole: When Murphy is in the changeroom at the station, he learns that an officer has just died and that his funeral (according to the captain) would be the next day. There's simply no way a funeral can take place one day after someone's death. All the planning, prep work and getting the body released to the funeral home would take about a week...plus many other things. Simply cannot be done.
Plot hole: Murphy can't arrest OCP Executive, Dick Jones as it's against his Directive. But with the video recording of Boddicker admitting that Dick Jones is the man behind the murder of Bob Morton, any other police officer could have made the arrest anytime.
Suggested correction: Murphy's big mistake was trying to arrest Dick Jones himself (considering he had no idea that it was against his directives). After that fails, Jones has ordered the entire police department to destroy Murphy, which means he has to go into hiding. Even at the end, he still has to take Dick Jones down by himself. Now if Robocop had simply gone back to the police department and showed the evidence, things might have turned out differently. But his self-confidence turned out to be a huge mistake.