Some advice explicitly directed at less senior people. I would very much advise some who does not yet have tenure to NOT take the nuclear option (e.g. posting a paper on the arXiv accusing someone of being wrong, or writing irate letters to the editors of a journal). In the extremely rare cases in which this has to be done, it is best done by someone who is both pretty senior and very politically skilled. This leads me to my other piece of advice. Namely, talk to other, more senior people in your research area. First, they might be able to convince you that it isn't really as serious an error as you think. Second, they will probably know the personalities involved better, and be more effective at convincing an author to do the right thing if something has to be done.
The two times something like has happened to me, I had ended up proving stronger results than the erroneous papers by pretty different techniques. I buried remarks at the ends of the introductions of my papers mentioning the wrong papers and explaining where they went wrong. On one of those occasions the author had left math and I didn't know how to contact him, so I didn't correspond with him first (after I posted the paper the arXiv, one of his friends contacted him and we exchanged some friendly emails). The other time, I explicitly cleared the language I used with the original author.
Nobody seems to have mentioned much about teaching--- perhaps because the original question itself makes no mention of teaching having anything to do with the desire to return to academia. This is a kind of elephant in the room.
I should admit: I'm on the academic side, I have not personally tried to make this kind of transition, and I have never been in a position to evaluate somebody making this kind of transition. But it seems to me that if you're reasonably current with your research area, and publishing papers, and meeting people (as suggested elsewhere), your biggest obstacle may be teaching.
Presumably you have no teaching experience over the last n years, and depending on your grad school experience, you may not have had much then (or it may have been a different sort from what professors do). This may matter. I don't know how to begin building a teaching history, while working a full-time job.
You may need to overcome the suspicion that will find teaching low-level service courses boring for the same reasons you find your current job in industry boring. Imagine the skeptic on the search committee who asks, rhetorically, "Who wouldn't be an academic if it were all just learning, writing papers, and talking to enthusiastic people with the same interests?"
Even with stellar references and a personal connection or three in the department, someone will ask: can you teach? Do you want to? What's the answer, and how do you convey it on your CV?
I don't have specific advice in this area, because it depends on where you want to work, and your own background. If it is possible to do pedagogical things in your current job, or service/outreach to non-specialists or students, perhaps that would help. Maybe actual teaching (on a per-course basis, not as tenure-track faculty) or volunteering would help. My feeling is that you need to do something to address these issues head-on, to confront both any genuine gaps in your CV, and the biases and prejudices you may face simply because you are changing careers.
Best Answer
Understanding old results and putting them into new perspective has its own very important value. You should not underestimate it.
However, especially for a novice, it is difficult to judge this. Consult your reviewer and ask for advice. If an experienced and well-established mathematician sees value in your work, then you should try to publish it.
Of course it is an important and difficult question where. Not all journals approve of this type of synthetizing papers. Here again, the help of an experienced established colleague is inevitable.