"Perhaps it is time we inform the Senate that our ability to use the Force has been dimmished."- Mace Windu
I think, for a long time up to this point, the Jedi Order was off it's game, in the cosmic sense. It simply wasn't a time for Jedi anymore, and they were so desperate to keep whatever they had that they pushed unreasonable expectations on the younglings and while they came out of it ok, its certainly not healthy.
At the time, the Jedi Order was made mostly of diplomats and the like that had never seen a war much less be involved in one, save for the eldest of the members, specifically, those on the Council. Its no wonder a great deal of them dropped like flies in the collesium battle near the end of the Episode II.
Its not their fault however. And ultimately, I don't blame the Jedi either, I blame the government which the Jedi are subjected to. And what was the government? By this point it was corrupt and complacent.
Windu said it best himself "we're keepers of the peace, not soldiers."
That being said, we cannot necessarily blame the Jedi directly or their mindset and reluctance to allow Anakin to be trained. Remember, they are working under the impression that he MAY be the chosen one who will bring the Force back into balance and he's just too great a liability. Their holding him back may not seem fair, but their concern is genuine. Yoda especially can feel Anakin's pain and frustration, so he knows perhaps better than anyone even Kenobi, that Anakin is unstable and should be closely watched.
The fact is, he is NOT the chosen one, and Qui-Gon Jinn was right when no one thought he was. Anakin would BRING balance, but it wouldn't be him, but his children, specifically Luke and his reinstitution of the Jedi Order, and a Jedi Acedemy. Qui-Gon somehow knew this about Anakin, whereas they saw it as a blind faith he was putting in the young boy. One Jedi was able to see what a council supposedly made up of the strongest Jedi could not.
Their minds were not in the right place at the time, as Sidious would have it.
Remember, the Jedi Order we see in Episodes I-III is based around a government that is not working and is flawed. In the process of protecting it, the Jedi themselves became flawed and perhaps too content. What wasn't their concern they didn't deal with, they let it pass.
They conformed to the standards of the government they represented, and thats the mistake. They became an organization within it doing what is self-serving.
You are what you eat.