Another thing Moat was guilty of was being an idiot. He shot his girlfriend's bloke believing him to be 'the copper that sent him down'. Well he wasn't, was he. Best to get these things right before you go on a shooting spree really.
Not only that, but so what if he had been a copper? Moat's vendetta against the police was outrageous prejudice; imagine how the public would view him if he'd targeted prostitutes or blacks.
Finally, what was his girlfriend actually guilty of? By pursuing his course of action, Moat pretty much completely confirmed why she was right to leave him in the first place; he was a psychotic control freak taken to performing the most heinous acts of violence against those closest to him, for things which never took place. Which is also a pretty good reason why his brother shouldn't have been allowed to go near him at the end, because Moat might have shot him too for all we know.