Off course you should. It's not like a boss is a god or something. Are you Japanese? Japanese folk are like that. If you are Japanese then the proper thing to do if you disagree with your boss is hara-kiri because no Japanese can live with such dishonor, or so I've heard. Japaneses are awesome like that.
Depends on the ownership and jurisdiction, and if you have an actual collaborating expertise to back up your disagreement.
For example if you are the technical expert on a specific process or have an establish ownership to a certain work or task then you can correct your boss if you think he misunderstood or misinterpreting some technical information, procedure, or results.
However if you think you are smarter than your boss in terms of how he should perform his supervisory tasks then that's not part of your job anymore. And that is not "correcting a fault", that is complaining.
If you have an issue about your boss management method or if you think you have a better ways of doing things,
it would be better to bring it to some neutral third party or to the upper end of the leadership ladder that could intercede between you and your boss rather than to assume you are correct and your boss is at fault.
If those are not available, I think it would be better if you give your boss an "advise" rather than to straight point out that you are way smarter and your boss is dumb.