Looks like Wayne Fincher appealed his case based on Heller, and lost, based on the reasoning that machine guns, which are banned, aren’t in common use, which makes their being banned constitutional.
Lots of back and forth in the comments about the absurdity of the ruling. I agree with folks that the “common use” test proffered by Heller is insufficient, but I think a way around it, without having to blatantly overrule it, is to suggest that one must look at police use, when determining whether an arm in question is protected. If an arm in question is of a type that is part of the ordinary equipment of police work, it must necessarily be protected by the second amendment. Of course, this doesn’t necessarily get you machine guns, as I’m not certain whether machine guns are common police equipment. But it does get you out of the trap where the government could prohibit or frustrate commerce in new arms technology before it becomes “common” and then not worry. If it’s a useful instrument for self-defense, police departments will probably pick it up, and it will become common. Note that I don’t think you have to show that every patrol car has one, just that it’s not unusual, or unheard of.