@Verus:
Because if you are correct, Fujitora will not attempt to arrest Doflamingo, nor will he hamper him in any way, before receiving permission from headquoters.
I mean, he could always change his plan (again), but yes, as things stand, I expect him to not interfere with Doflamingo until after the birdcage comes down and he's able to communicate with them. The conversation may again occur off-screen, but if so, I expect we'll hear something about it again (like Tashigi's speech).
Though, from pure intution standpoint, I have to say, I find it slightly silly that an Admiral can order a total destruction of one the three biggest goverment facilities on a whim, and by proxy, and not have his orders questioned in any way,
I presume you mean "by the authorities after the fact", so I'm going to answer in that vein. CP9 was part of the World Government's Cipher Pol intelligence apparatus, and the director answered to the World Government, not the Marines. He convinced them to let him go after the Ancient Weapon; if Aokiji gave him access to a single buster call to aid in this effort (and may well have been expressly authorized to do so, for all we know), then I expect any blame would fall upon the shoulders of the CP9 director. Aokiji was simply providing assistance to an intelligence operation that was out of his chain of command entirely.
And the Marines tend to play fast and loose with the rules without getting in too much trouble for it. Garp pretty much did whatever the hell he wanted, and I'm pretty sure plenty of it wasn't technically allowed, but who's going to call out Garp the Hero for breaking the rules? I'm not saying Fujitora couldn't break the rules and arrest Doflamingo now and likely get it approved after the fact, I'm saying he's intentionally being legalistic in order to let Doflamingo make the mess bigger.
but is not within his authority to act against known psychopath ex-pirate
Who is also the "legitimate" king of the World Government country on which they are standing, and an ex-Celestial Dragon who still has strong connections.
Though, if the solution was that simple, one would think he would said it to Maynard, instead of being cryptic.
Maynard expressed moral outrage, and he responded to that moral outrage by asking if the World Government is some kind of god. Then he told Maynard to, essentially, shut up and follow his orders. Maynard is an underling, Fujitora doesn't have to explain shit to him… and telling him his real plan would simply provoke more outrage from him, and possibly cause him to attempt to undermine the plan.