Why did the Jedi fail to get information about Order 66?

Judging from Battlefront 2, but I am not quite sure it is canon, they knew it from beginning and they believed they should kill the jedi. Although there were splinter groups who said no, and some of the clones were reluctant to kill some of the jedi. But like I said, I am unsure if this is canon.

While there seems to already be an accepted answer, and I am far from a master of where the current canons lie, I would not be surprised if some or all of the Jedi were aware of Order 66 and felt that it didn't apply to them. It's human (and quite possibly alien) nature to look at a law stated to target a group of bad people and to assume that you would never be designated as such a bad person. The Jedi know that members of their group have gone power-mad. They know that Jedi have turned to the Dark Side. Why would they object to a measure clearly built to defend people against such abuses?

I suspect there were no objections to this rule because it sounds perfectly reasonable, if you don't know how it is going to be carried out.

In the event of Jedi officers acting against the interests of the Republic, and after receiving specific orders verified as coming directly from the Supreme Commander (Chancellor), GAR [Grand Army of the Republic] commanders will remove those officers by lethal force, and command of the GAR will revert to the Supreme Commander (Chancellor) until a new command structure is established.

The way it is written, it sounds like a perfectly innocent contingency for in case any Jedi officers go rogue and become a threat to the Republic as a whole. And given that the Sith were clouding their ability of foresight, they had no way of knowing that this order would be given to every GAR commander at once, thus ordering the mass execution of the Jedi. You have to remember, until that very moment, the Jedi trusted the Emperor and believed him to be benevolent.

Well they could have because some clones like fives tried to tell them but then got killed off. Its probably just that they were all focused on the battles, because some Jedi like Ki-Adi Mundi got killed when they were fighting, but some of the Jedi did because don't forget Anakin launched on attack on the Jedi. They all thought Anakin was on their side and he started killing them and all but not all the Jedi didn't know what was going on.

The clones had chips in their brain that made them cooperate with order 66. The Jedi can only sense threats that they can expect. So the clones executed most of the Jedi and then the rest of the Jedi on Coruscant witnessed the Supreme Chancellor (Darth Sidious) revealed his real self a Sith lord! then after then the empire was born.

There are 150 contingency orders. Considering the clones learned a lot of their information by flash memory programming, it's very likely all 150 were "burned in" just as many combat tactics would have been. From before being released from the stasis/cloning chamber they are being implanted with memory. After being released, about age 5, I think, they do nothing but train. So, it's no surprise the orders would be committed to memory just as ingrained as anything, just as natural as eating or walking.

Why didn't the Jedi know about Order 66? They did. All 150 orders would have been presented to the Senate and passed. Debated upon and passed. I doubt they gave it more than a passing thought. As noted, it does not order ALL Jedi to be killed. Just whichever one the Supreme Chancellor orders eliminated. Or ones. Or, if he issues the order 50 times... then 50 Jedi. Which, if you notice, he specifically orders Commander Cody to eliminate Obi-Wan. He gives a specific individual order to the clones that are with Yoda, Secura, Mundi, and Koon.

I'd theorize that, especially for the Master Jedi, Palpatine issued the orders to EACH clone commander individually and personally. His one major mistake... he should have given the order to eliminate Yoda first. Then Obi-Wan and then the others. This is because Yoda, of all the Jedi other than perhaps Mace, is more attuned to Living Force and to being able to precognate and to feel the other Jedi. He was constantly aware of the other Jedi in the Force. He felt Anakin's pain on Tatooine when Mace and Obi-Wan couldn't. I'd also theorize it is why Qui-Gon was able to make contact with Yoda. Yoda naturally was tuned to feeling the Force in others more than the other Masters.

So, the Jedi didn't detect Order 66 as a threat written in a group of 150 other orders because there's no reason to consider it. Much as most Americans have no clue what Executive Order 11490 or 12919 says, does, or means. Why should we? It's just another mess of bureaucratic stuff we don't need to pay much attention to... until it gets implemented. By then it's too late to think about it. And the Jedi didn't detect any threat form the Clones because they didn't hate the Jedi nor have any ill or harmful feelings towards them. An order to shoot and kill is just as non-emotional for them as an order to dig a trench. The Jedi feel when a person is threatening. The clones weren't. They were just following orders. By the time they were, the Jedi was already in the cross hairs and pretty much toast.

As you might recall, Chancellor Palpatine convinced the Galactic Republic that the Jedi were power-thirsty criminals, and he managed to dissolve the Jedi Order. Soon after, the Jedi Purge began after Order 66 was enacted. So, while the Jedi were being hunted to extinction, the specifics behind why the Clone Troopers were killing them off (Order 66) was fairly insignificant to them.