How does the novel portray that power should always be distrusted, in whatever hands it is placed?
In Fahrenheit 451, one of the lessons is that those in power (not power itself) should always be questioned. So, there should be what you might call a "healthy distrust" of authority in order to do two things: to keep the citizens aware of the social conditions of their lives and to keep authority figures/groups from stifling that awareness.
In the novel, those who become aware or question the social conditions in which they live (Clarisse, her family, Montag, and Faber) are claimed as enemies of the state (authorities) and sentenced to death/arrest. The novel illustrates that a society in which authority cannot be questioned or challenged can lead to a passive, thoughtless citizenry. The immense power of the authorities in this novel exists because those authorities have been successful in pacifying the citizens and subsequently because those citizens have not challenged those authorities. So, the novel does propose that a healthy mistrust of authority figures can limit the power of the state to necessary levels and that mistrust also keeps the citizens aware of the pros/cons of their social conditions.