Scalia himself went into some detail about the dubious right of citizens to own military-style weapons, and the legality of various existing regulations.
Justice Scalia in re Heller:
“It may be objected that if weapons that are most useful in military service — M-16 rifles and the like — may be banned, then the Second Amendment right is completely detached from the prefatory clause. But as we have said, the conception of the militia at the time of the Second Amendment’s ratification was the body of all citizens capable of military service, who would bring the sorts of lawful weapons that they possessed at home to militia duty. It may well be true today that a militia, to be as effective as militias in the 18th century, would require sophisticated arms that are highly unusual in society at large. Indeed, it may be true that no amount of small arms could be useful against modern-day bombers and tanks. But the fact that modern developments have limited the degree of fit between the prefatory clause and the protected right cannot change our interpretation of the right.”
The prefatory clause to which the justice refers, of course, is the one about “a well-regulated militia.” The AR-15, used in San Bernardino, is an M-16 knockoff.
So rather than saying “assault weapons,” in the future perhaps we should say “the kinds of weapons that Justice Antonin Scalia has defined as ‘dangerous and unusual’ and subject to regulation or an outright ban under the Second Amendment.” From the NYT Dec. 11, 2015
This wasn't an egregious decision, IMO, but it shouldn't be held up as a blanket approbation of any and all firearms. Heller was a peace officer--you might say a member of a militia, which put an interesting spin on it.