Regarding Feinstein's words as given in the OP...
Justice Scalia also wrote that, ‘Weapons that are more useful in military service, M-16 rifles and the like, may be banned without infringing on the Second Amendment.’
This transcription is wrong. Feinstein actually said, "...Justice Scalia also wrote that, quote, weapons that are most useful in military service, M-16 rifles and the like, may be banned, close quote, without infringing on the Second Amendment..."
As Frank Ettin pointed out in post #5, the quote that Feinstein there took from
Heller was not, as she presented it, a conclusion of the majority, but was instead part of a conditional clause (she omitted the "if"). So, Feinstein misrepresented
Heller.
I think that it is likely that Scalia wrote the opinion as he did because he was a precise writer and he wished to make it clear that the majority was limiting the scope of their decision to the laws challenged in case at hand (the DC handgun ban and the DC ban on keeping guns at home if they are unlocked and functional). We can speculate as to whether such an explicit limiting of scope was required by one of the other justices, to get him to sign on to the majority.
The majority in Heller does seem to indicate that certain firearms can be subjected to the tax and registry requirements of the NFA:
We therefore read Miller to say only that the Second Amendment does not protect those weapons not typically possessed by law-abiding citizens for lawful purposes, such as short-barreled shotguns.
It is unclear to me whether, in accepting the current restrictions on SBSs, the majority also implied that the current ban on machineguns, via the Hughes Amendment's closing of the machinegun registry, was also constitutional.
True: the opinion seems to recognize a
Miller-imposed limitation of 2nd Amendment protections on arms:
We also recognize another important limitation on the right to keep and carry arms. Miller said, as we have explained, that the sorts of weapons protected were those “in common use at the time.” 307 U. S., at 179. We think that limitation is fairly supported by the historical tradition of prohibiting the carrying of “dangerous and unusual weapons.”
Still, I note that the cited "historical tradition" concerned banning
carry, not ownership; for example:
The offence of riding or going armed, with dangerous or unusual weapons is a crime against the public peace, by terrifying the good people of the land
Source:
http://www.bc.edu/bc_org/avp/cas/comm/free_speech/blackstone.html
So one may well consider whether the 2nd Amendment does indeed protect the
ownership of machineguns, even supposing that they are to be considered “dangerous and unusual weapons.”