Let's review,
He shoots through his ceiling and into his neighbor's apartment. He claims it's a cleaning accident while the neighbor claims it was intentional.
I suppose I could have been generous enough to give him the benefit of the doubt in this case, though if the prosecutor really wanted to he could have probably charged him with something like reckless endangerment
He shoots out the tires of a neighbor's car claiming that he "blacked out" in a fit of rage.
Charges should have definitely been filed in this case. At the very least, property destruction and unlawful discharge of a firearm would be appropriate and, honestly, I don't think that assault with a deadly weapon would be inappropriate. Also, if his claim that he "blacked out" in a fit of rage was believed, then that should meet the legal definition of "a danger to self or others" to justify involuntary commitment to a psychiatric ward.
From what we've heard, he had multiple disciplinary actions taken against him and was forced out of the Navy yet still received an honorable discharge.
I'm not knowledgeable enough about military discipline to be able to comment on whether or not his disciplinary problems would have been severe enough to warrant a dishonorable discharge. However, I do know that a dishonorable discharge is comparable to a felony in that it makes one a prohibited person under the Gun Control Act of 1968.
According to several sources including CNN and the UK Daily Mail, the only weapon that was brought to the Navy Yard by the shooter was a shotgun, specifically a Remington 870 per the UK Daily Mail. All other weapons used appear to have been obtained from security/police that were shot on site. Furthermore, the shotgun was purchased from a dealer and the shooter presumably passed a NICS check to obtain it.
I don't recall seeing pump-action shotguns on any assault weapon ban lists. As a matter of fact, even under the NY SAFE Act which, which gun-control advocates proudly promote as the toughest in the nation, said shotgun would still be legal.
So, in review the shooter appears to have started his rampage with a gun that would still be legal even under Sen. Feinstein's AWB and any "assault weapons" used were obtained from the police/military, which even Sen. Feinstein isn't advocating disarming. Furthermore, we have at least one, if not two chargeable offences in the shooter's past as well as ample legal justification to involuntarily commit him and possibly severe enough discipline problems to warrant a dishonorable discharge from the Navy any one of which could have been used to place him on the prohibited persons list therefore denying him the ability to pass a NICS check.
So, it appears to me that neither the AWB nor the universal background checks that Sen. Feinstein wants could have prevented this incident since the shooter apparently passed a background check and did not, initially at least, use an assault weapon. Perhaps if Sen. Feinstein had waited to learn even a few of the facts, her comments wouldn't seem so asinine. Of course the facts seem to indicate that the blame for this incident lies in multiple failures to enforce existing laws rather than the need for new ones, but that doesn't fit Sen. Feinstein's agenda.