To command Camp Mirage he would have to have had a Top Secret clearance. That requires interviews by CSIS, not psychs, including interviews and background checks of family and friends. The concern is whether there is any reason a guy could be blackmailed or might take actions to betray his country. Its a security clearance not a mental clearance. The mental clearance is much looser. When a person enrols in the CF he is screened by a series of tests - aptitude and psych are part of them, and a number of interviews with questions written by experts but administered by Recruiters. To that end the CF is very effective at screening out the weirdos who want to join the Army to kill brown people or to boss people around or are at risk of "losing it" with a machine gun. They don't want that at all, despite what people whose only knowledge of the military is having watched Full Metal Jacket 19 times, might think.
After that, there is occasional psych screening but it is more aimed at general mental health and well-being, trying to determine whether a guy has PTSD or if a family or stress-related situation could impact his ability to do his job. The (untrained in mental health) chain of command used to be able to make assessments of a person's general mental health but being a fluffy socialist country, those with apparent problems are now referred to a case worker and the chain is not ALLOWED to know what's going on in a guy's head. The member's privacy is more important. The chain of command is simply told whether the has any employment restrictions. These assessments are usually done by civilian mental health doctors, if someone is felt to be "off" or if he self-identifies as having a problem. But, for the most part, a guy like Williams wouldn't undergo any serious head tests and if he did, it was likely administered by a social worker and like I say was simply to determine whether he was too stressed to do whatever job he was up for.
As a pilot, he may have had a few more detailed tests administered than a more typical soldier/sailer/airman would have, but I am not sure. And, those tests would have been designed to determine his ability handle cockpit skills such as multi-tasking, rapid assessment and decision making, effectiveness under severe stress and time constraints, stamina, etc. Are these similar aptitudes of a serial killer? Maybe. But, like I think aardvark said, 800 000 other people with those qualities WON'T go on to kill anyone.
This guy must be a VERY DEEP psychopath. Throughout his career he would have been working in very close proximity to A-type personalities, hard working hard chargers with high performance standards. Both in squadrons and on courses he would have been working and playing in very tight proximity to guys who would have had ample opportunity to identify if a nut was loose. It would also have come out in the decisions he made and his interactions with his peers and superiors. Who the hell can screen for that type of mental defect though? If he was simply a 'weirdo' that would have been known and he likely would have failed to progress much in rank. But no one goes into a work relationship wondering whether a guy is a serial killer.