That said, what I want to hope will come out of this would be a closer look at our mental healthcare system. It's a disgrace.
This, pretty much. Unfortunately, spending money to help people seem to be extremely unpopular in this country, so I don't expect things to change anytime soon.
I don't think that would've helped, since this guy was pursuing his PhD in neurobiology and already had his masters degree. That implies that he got through at least six-years of close, almost daily contact with experts in mental health, psychology, neuro anatomy, and any other expertise you could throw in there.
If we were watching people more closely, he would've been one of the "watchers." He had far less red-flags than the Fort Hood shooter, who killed 13 on a secure military base. Between the two of those cases, it's a safe bet that there will always be major holes and we'll never stop all such attacks.
Likewise, the guy was making bombs, so even the most draconian gun restrictions wouldn't have completely stopped him. If he'd focused on barring the theater doors and using incendiaries, he might've killed almost everybody, similar to the Beverly Hills superclub fire (165 dead), the Cocoanut Grove nightclub fire (492 dead), or the Iroquois Theatre Fire (602 dead), although I don't think the modern, open, sparsely furnished movieplexes we have now are nearly as flammable as the ornate wooden theaters used to be.