It's heavily implied that powerful government figures sent the assassin to try and kill Tayo. But this makes no sense, since those people could just fire him, which is completely legal and also a foolproof way of keeping him from implementing the system.
The agents say that Vivienne is to be arrested because her unpublished book advocates revolutionary violence. She denies this, but even if the accusation were true it would not be grounds for arrest. In the US it is not illegal to advocate the overthrow of the US government. To establish conspiracy, the FBI would have to demonstrate that Vivienne, and at least one other person, had committed "overt acts" in furtherance of those aims, such as buying weapons of planning assaults.
It's said that the AI system is directing people to be arrested based on their likelihood to commit crimes in the future. Regardless of the computer's ability to predict future crime, there is nothing in US law which allows for someone to be arrested for crimes they might commit.