One thing that's worth noting about the AG's speech, before commenting on the deeper problems.
While 'terrorist' is a broad and poorly defined term, the AG is using it as shorthand for those targeted by the
AUMF. This gave the president power to wage war against a certain group. Specifically;
That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons.
This is the definition that is in question in all these points of law. Holder's speech specified that the targeted individuals must be part of al Qaeda or an associated group to be sure of satisfying this definition.
The main point of that speech was to defend the legality of using against US citizens overseas what have been effectively accepted as legal actions when used against non-citizens.
Abstracting this further, I'm not sure I'm entirely opposed to the administration's logic here. Their argument boils down to these being military strikes against military targets. The decision to go ahead with one of these strikes does tend to be a military action, made with little time and based on changeable conditions and intelligence. If a US citizen had joined the ground forces of an enemy power I doubt you would have a due process case to make when he is killed in combat, even if his citizenship was known when the shots were authorised. The way the administration has laid out their case is dragging these extra-judicial killings towards that sort of case. Which is to say that their full set of conditions requires a situation that most people would probably agree is a military strike against a justified target where judicial review is impractical or even impossible.
I'd probably be more comfortable with the situation if there was guaranteed retroactive review, with the administration being required to put their case before a judge simultaneous to the strike. It might not prevent the first unjustified/illegal attack, but it would allow for consequences to such an action while also preventing or at least discouraging others. At the same time that might be enough to discourage the US from taking any such open actions. I don't doubt that this would force any such targeted killings underground rather than actually stopping them.