Waingro's problem was that he was just a stone cold nutjob killer. He shot the 1st guard, who was clearly disoriented and making no overt threat, after being warned that the guards couldn't hear him. It seems correct that he had already killed at least 2 women for no reason before he broke discipline during the armored car robbery.
McCauley would have been better off dumping Chris, but for the fact that Chris appears to have had necessary technical expertise, and for the fact that the movie seems to make the point that his weakness is a lack of discipline in life, but not in his "work."
The real screw-up, which seemed to be highlighted pretty brightly, was McCauley's violation of his own rules, which happened twice (at least twice with consequences). 1. Proceeding with the bank job after becoming aware that they were under surveillance, and 2. Acquiring something he couldn't walk away from in 30 seconds flat - in this case, not a house or dog, or even Amy Brennaman, but his need for vengeance against Waingrow & the financier-guy. That is the central irony in the movie: while he deprived himself of the normal comforts of life in order to be ready to flee at the drop of a hat, it was in the end attachment to [i]hatred or pride [/i] that rooted him to the spot and led to his death.