There are many serial killers who have functioned for YEARS in society without being detected by their acquantances, neighbors, families, wives, etc. Look at Ted Bundy, John Wayne Gacy, Gary Ridgeway. They may have been seen as a little eccentric, but no one thought they were capable of one murder let alone as many as they did.
I agree with Julie (TWICE in one week - can ya believe it?!?! LOL). There is only one person who bears true responsibility on this one - the killer himself. His parents weren't psychologists or criminal profilers. It's not like there is some kind of checklist or pamphlet that is sent home to all parents: "What to look for in a future serial or spree killer."
How many of us, who (as far as I know) all turned out OK and haven't gone on any killing spree, went through a difficult or despondent phase as teens, pulled away from our families, changed the people we hung out with or at least cut off contact with childhood friends? OK, yes, the triad of predictors for serial killers probably wouldn't apply (late childhood bedwetting, starting fires, cruelty to animals). But for spree killers? I don't think there even IS a commonality list that parents could look for.