I can't find a link right now, but a bit of reading between the lines of Acts also brings quite a few questions, even though the spin there is in Paul's favour. (And some of the dead see scrolls seem to be extremely bitter against one who leads people astray from the faith, presumed to be Paul.)
For a start, while James did give Paul dispensation to not _require_ a full conversion to Judaism by the Gentiles or circumcision, what Paul does is outright preach _against_ it. E.g., in Galatians 5:2, 6:12-15, Colossians 3:11, he not only thoroughly dismisses its necessity, and calls those who want to circumcise you as just trying to get some glory for themselves out of it... but also makes it pretty clear that there is no difference between Jewish Christians and Gentile Christians in that aspect either. Basically even the Jews don't need it any more, according to him. Jamese had simply not given him such dispensation.
Also while James did require _some_ minimal dietary laws even for gentiles (e.g., no blood), Paul doesn't mention that in any of his epistles, and in fact considers the whole of the OT to be now null and void. In fact, far from being a temporary dispensation for Gentiles, Paul seems to think it doesn't apply to Jews any more either, as seen in his rebuking Peter for going back to the dietary laws after a meeting with James. (Galatians 2:11-12) And in Galatians 2:15-16, he insists that, basically, keeping the law is no factor in salvation, apparently not even for Jews like him or Peter. And ends with a climactic declaration that "
for if righteousness come by the law, then Christ is dead in vain."
Again, James had not given him authority to fully abolish the OT, and certainly not for Jews like himself or Peter.
Understanding this helps in understanding what James requires of him in Acts 21.
For a start, if James too saw Christianity as that radical a departure from the Law, it would make no sense to require Paul to prove his faith to non-Christian Jews. Knowing that some non-Christian mob wants Paul dead would make it more logical to just get him out of town ASAP, not make him appear in front of a mob.
Likely, James and the Christian Jews too want to see Paul prove that he still keeps the Law. At any rate, that's what they require him to do. (Acts 21:24)
That's the people who are concerned "
that thou teachest all the Jews which are among the Gentiles to forsake Moses, saying that they ought not to circumcise their children, neither to walk after the customs." (Acts 21:21, My emphasis.) While James repeats his dispensation that the _Gentiles_ need not be forced to circumcise, and only get a reduced set of dietary laws (Acts 21:25), this charge is that Paul had been teaching _Jews_ too to disobey the Law. Something he had no right to do.
So essentially he's put under the escort of four men, to undergo a purification ritual and sacrifice and generally show that he still lives by the Law. It doesn't sound to me like the Christian Jews under James were that OK with Paul's vision than the OT is completely obsolete, and this time they even do something about it.
(It also kinda makes the point that Paul's proclaimed version of what great stuff he did for the Gentiles in Acts 21:19 and they liked in the first half of Acts 21:20 omitted those parts. Must have slipped his mind

)
Making him appear in the temple and in front of a multitude in the process, and in fact prove his observance of the Law _to_ that multitude, also makes it pretty clear what would happen if he fails. Even if James's followers themselves wouldn't stone him personally, that's what would happen. Essentially James is at the very least OK with that outcome if Paul fails to show his adherence to the Law.
But at one point a bunch of Jews from Asia (likely Christian Jews too, since they had paid attention to what he was preaching) make a big fuss about what Paul actually does preach: "
This is the man, that teacheth all men every where against the people, and the law, and this place" (Acts 21:28). Again it seems an interesting choice of words that they say he teaches _all_ men against the Law, as opposed to, say, merely that he teaches the Gentiles against the Law, which everyone involved likely wouldn't have given a damn about.
Paul gets nearly killed, but he gets rescued by a Roman patrol: "
And as they went about to kill him, tidings came unto the chief captain of the band, that all Jerusalem was in an uproar. Who immediately took soldiers and centurions, and ran down unto them: and when they saw the chief captain and the soldiers, they left beating of Paul." (The presence of centurions -- roughly equivalent in rank to a modern Colonel - kinda makes it sound like a small army jumping to the rescue. But I digress.) The wording "as they were about to kill him" and the fact that the Romans had time to intervene, makes it sound not like an impromptu assault on Paul, but rather like they were about to do it properly.
It's also interesting that at this point there is no mention any more of James or his followers or even the four men who were seeing to it that Paul completes his ritual. The whole Ebionite sect had exitted the scene. It seems to me like they had taken their hand off him, and left him to his stoning. And not the herbal kind.