Also, what w4 said. But again if you want to get technical, the Constitution restricts Congress's authority to provide for the common defense to having an army or a navy, but not an Air Force, and not a National Security Agency.
There's some scary stuff in the farming regulation. There was a law in the works called NAIS (national animal ID system)that severely intrudes on people's right to raise their own livestock. It was stirring up a storm of controversy in homesteaders' circles a decade ago, though I don't know the current state of that is.
While, the court process and decisions occurred during WW2, the law and the acts which, under it, created the controversy occurred before US involvement in WW2, it was more about the Great Depression/New Deal than the War.
I will go back and reread it to see whether that impression is correct or whether I've imputed my own bias to the court's decision since I read it, but given that I'm generally of a more statist bent than most people here I don't think it's just personal bias.
Actually, virtually all of Congress' enumerated powers are in Article I, Sec. 8. The interstate commerce clause, specifically, is unlikely to be cited in a defense of the NSA -- more likely, the Necessary Proper Clause of Art. I, Sec. 8, along the military powers in the same section (and the obligation to protect the states against invasion in Art IV, Sec. 4) would be more likely -- those who view the designation of the President as Commander-in-Chief of the military in Article II as a power of that office might be inclined to cite that "power" along with the Necessary and Proper Clause of Art. I, Sec. 8, instead.
It allows Congress to raise "Armies" (plural) and a Navy, and it allows Congress to choose how to equip and train the Armies it raises. I don't see that it prevents it from choosing to a equip one of the armies primarily with fixed-wing aircraft, training it in doctrine for employment of such equipment, and give it the name "Air Force" to distinguish it from other armies that are differently equipped and trained.