OK. So what I've done below is listed each of the amici and summarized in my own (brief) words what I think is the "gist" of their arguments. Later, I will try my hand at interpreting the bigger picture or overall scheme. Note that these summaries are based on each brief's own summary of the argument, and in some cases, their introduction to the argument.
That said, part of my response shall regard the frequency and urgency with which the incorporation question is brought up....very interesting.
Amici for Petitioner - listed in order of appearance here: http://dcguncase.com/blog/case-filings/
Janet Reno, et al.
[2A protects rights only related to militia; Miller (1939) established (or at least confirmed) that; individual rights ruling would jeopardize federal gun control; such would limit ability to control crime]
National Network to End Domestic Violence
[Domestic violence is terrible (while it is terrible, argument appeals mostly to emotion); handguns often used in domestic violence; thus, banning them is justified]
American Jewish Committee, et al.
[Court below erred in its interpretation of the 2A; argues that the 2A protects state authority from the federal government; does not bar states and localities from protecting their populations (via gun bans)]
States of NY, HI, MA, MD, NJ and PR (OT - Puerto Rico is a state?)
[2A not applicable to state law, and no reason for it to be; 2A drafted to ensure federal government could not disarm state militias; amici states do not endorse handgun ban; argues against incorporation]
American Bar Ass’n
[Argues the importance of stare decisis in case law; as case law declares the 2A pertains only to militia purposes (cites Miller, 1939), ruling that it protects individual rights violates the principle of standing case law and as such lower court’s ruling should be overturned; failure to do so would call into question the constitutionality of “established” gun control laws]
Brady Center
[2A protects ownership of firearms only in the context of the militia; 2A was not meant to protect private ownership of arms; this was settled in the Miller (1939) decision; right to be armed for self-defense is “dangerous”; legislature is best to decide firearms prohibitions, not the judiciary]
U.S. Department of Justice (this might be the most significant brief...certainly among the most significant)
[2A protects right of individuals unaffiliated with militia to possess firearms; prefatory language does not negate the operative guarantee; court below erred in applying a categorical standard by which to evaluate protected arms/rights; argues that current federal gun control is established and important – SCOTUS decision should/must not be read as way to allow attack or invalidation of federal gun control legislation; banning NFA weapons is consistent with legitimate government interests; the issue of the scope of the 2A lacks case law and thus the issue should be remanded down the courts to flesh out detail and standards]
18 Members of Congress
[decision below read the 2A to create an individual right to possess firearms unrelated to militias; Miller is settled precedent in that 2A protects arms possession only in militia service; Note – these amici bring up incorporation but take no position regarding the question]
NAACP Legal Defense Fund
[the 2A has always been interpreted to permit governments to categorically prohibit particularly dangerous weapons; does not protect individual right to possess arms; handguns need to be prohibited because, in part, lots of black people use them to kill other black people]
Criminal Justice Professors
[bans on handguns are effective in reducing crime and violence – criminology studies have proven the DC ban has done so; effectiveness of DCs law would increase if surrounding states were to likewise ban handguns]
DA’s for SF, NY
[that the 2A does not restrain current gun control legislation, because A) 2A does not protect individual right, is not incorporated, and C) current restrictions are reasonable; that overruling the DC ban will have negative and unintended consequences]
American Academy of Pediatrics
[children are susceptible to injury or death due to handguns; thus, the ban should be upheld]
City of Chicago
[non-incorporation of 2A is settled law; 2A does not protect individual rights; if individual right, does not prohibit Chicago’s handgun ban (because of non-incorporation); Chicago is very concerned because her laws are very similar to DCs]
Winkler, Chemerinsky
[if the 2A is ruled to protect an individual right, it must outline standards of review for reasonable regulation; reasonableness review standard is appropriate because gun control schemes are unquestionably legitimate means of enhancing public safety; claims the SCOTUS has held that the predicate for heightened scrutiny is absent; in the event of incorporation, any 2A standard more demanding than reasonableness review will [unacceptably] burden the states with litigation challenging prior convictions for weapons offenses; right to bear arms should be regulated as is the right to “property”]
American Public Health Ass’n
[firearms profoundly and negatively affect public health; social cost of firearms in society is high; public health approach is needed regarding gun violence – which basically reasons that violent crime is epidemic, guns cause this epidemic, thus, guns in society are an unacceptable cost to society]
Appleseed Center, et al.
[assumes (only, I think, for purposes of the brief) that individual right exists; court should allow local, elected officials to decide how to regulate firearms according to their particular needs (because this is the democratic way); under any appropriate conception of reasonableness, DCs ban is reasonable]
Violence Policy Center
[if the SCOTUS rules individual right, they must make this right subject to reasonable restrictions; DCs ban is reasonable because handguns are uniquely lethal and dangerous, and have (even) evolved to become more so since DCs ban was passed; handguns are less effective than other firearms for self-defense]
Cities
[gun violence is very bad; major cities bear the brunt of this badness and violence (argue urban v. rural); firearm regulation a critical aspect of cities’ valid and reasonable public safety measures; 2A protections apply only to federal governments, not city governments]
History Professors
[argue that evidence from the ratification debates clearly signify that the 2A was not meant to protect the rights of individuals to possess arms; any right to arms is certainly not a fundamental right]
Linguistics Professors
[militia clause is defined as an “absolute construction” or an “absolute clause”; it means that “because (and only because) the militia is necessary, the right to keep and bear arms shall not be infringed”; thus, the linguistics of the amendment dictate that right to arms is wholly restricted by the militia clause]