How can I deal with a significant flaw I found in my previous supervisor’s paper?
Two suggestions:
- You found that someone was wrong in a good journal. The fact that the error was published in a good journal does not mean that it is worth working on. You should decide if this error is really worthy of your research efforts. It might be better for you to work on something more important.
- If you decide to pursue the error, you can choose to present your correction as a new idea. If you tell people that you have found a new idea that advances the state of the art, that makes you look good. If you tell people you have found someone else's error, that makes the other person look bad but may fail to make you look good. The actual substance of the research can be the same, but the way you present it makes a world of difference in how it is viewed.
If you trust your previous advisor, I would:
- Talk to him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.
At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.
If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.
Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.
Unfortunately, depending on the topic, published mistakes can damage reputation (e.g. in math, as far as I know). This may, depending on topic, affect your advisor. Publishing a correction oneself can mitigate that. Other fields are less sensitive to honest mistakes.
So, the question becomes:
Do you have a good relation with your advisor? Then it were just an act of friendliness to give them the opportunity to fix their mistake. If you make it public, it means that you do not feel friendly enough to give them this opportunity and you feel that you need to go formal.
Which is acceptable and not wrong, but it clearly sends a message that you do not feel obliged to give your advisor the opportunity to rectify, in favour of getting a few pages in this journal, or else - as suggested elsewhere in the thread - that you do not trust them to do so.
The question is really if you think that this correction is so worthwhile to be published as standalone that you go possibly contrary to your old advisor and his friends.
To be sure: if one thinks something is seriously wrong with a given important research and the original researchers are not prepared to fix it, then one should report it (one has to balance this feel of duty with the fear of potentially ruining one's career).
But this is different from above: you do not know yet how they will react as long as you haven't given them the opportunity to correct the mistake. In this case, however, it is certainly not about getting a correction paper into a journal; the stakes are higher. Any backlash, if they are unhappy with your suggestion and you end up publishing a correction, would counteract any advantage from getting your paper into that journal. You should do this because it is the right thing, not because it advances your career.