Some excerpts from the majority opinion:
At a minimum, the government must make a substantial showing that the crime for which it seeks to try a defendant by military commission is acknowledged to be an offense against the law of war.
That burden is far from satisfied here. The crime of "conspiracy" has rarely if ever been tried as such in this country by any law-of-war military commission not exercising some other form of jurisdiction, and does not appear in either the Geneva Conventions or the Hague Conventions -- the major treaties on the law of war.
... (there is) a broader inability on the Executive's part here to satisfy the most basic precondition -- at least in the absence of specific congressional authorization -- for establishment of military commissions: military necessity. (Salim Ahmed) Hamdan's tribunal was appointed not by a military commander in the field of battle, but by a retired major general stationed away from any active hostilities.
Hamden is charged not with an overt act for which he was caught redhanded in a theater of war and which military efficiency demands be treated expeditiously, but with an agreement the inception of which long predated the attacks of September 11, 2001 and the [passage of the congressional Authorization for the Use of Military Force].
That may well be a crime, but it is not an offense that "by the law of war may be tried by military commissio[n]."