There is no prima facie ethical obligation correct the mistakes of others.
Any need to correct the mistakes of others would only arise due to other reasons. For instance, if you knew that a machine in a factory was prone to having its blade fly off in the direction of a group of people, you'd be under an obligation to do something about that (to the degree that your belief is certain and you have a capacity to do something).
Apart from variations on the above, you're not under any obligation to correct others even if erroneous equations are running around. Consequently, there's no research failing for your advisor not to publish it.
That being said, you would/do have an obligation not to propagate the errant equation. Since you know it's mistaken, you shouldn't include it in any of your publications as if it were true.
Similarly, it does seem questionable for your advisor to make his research decisions based on the interests of his company, but that's more a conflict of interest in general -- i.e. that he would put the interests of his company ahead of his research choices. Maybe to reword all of that into a few cases:
- Researcher A chooses to research and publish thesis P rather than thesis Q.
- Researcher B chooses to research and publish thesis P rather than controversial in field thesis Z.
- Researcher C chooses to research and publish thesis P rather than career-damaging thesis Y, because it will/might hurt his career.
- Researcher D chooses to research and publish thesis P rather than potentially business damaging thesis X, because it will/might hurt his wallet.
- Researcher E-1 researches thesis W, learning W may result in harm and does not publish it.
- Researcher F-1 researches thesis V, learning V will very likely result in harm and does not publish it.
- Researcher G-1 researches thesis U, learning U will undermine his business and does not publish it.
Actually, I don't think there's anything wrong with any of the cases above... but E-G are capable of wrongful variants. For A-D, we are not under any compulsion (generically speaking) to pursue any particular research agenda. Of course, we may be compelled by funding sources or bosses to do/avoid certain things and violating these sort of obligations can be immoral.
Skipping these employment obligations, E,F, and G can be immoral when we "and failing to inform relevant parties." In other words, if we have great reason to believe W will cause harm, then we should tell the company making it or the clinical trial using it. If U shows a business model is faulty, we should not defraud others with what we know is false.
tl;dr - without further complicating factors, there's no requirement your boss either research this further or publish about it.
Separately, it may make a great paper if you can show a well-cited equation is errant or needs updating. There, the challenge is knowing how to get it through in this political landscape.