This is a follow-up to my previous question: (Advisor's paper fundamentally flawed, what do I do?).
My advisor and another student collaborated on a paper. After reading it carefully myself, I've come to the conclusion that the approach, method, and analysis are all fundamentally flawed and the main result is plain wrong. A main result of the paper is a mathematical theorem. The paper was published in a peer-reviewed venue.
I've asked for clarification, which the authors (including my advisor) were not able to give. I've then pointed out the mistakes and errors in the approach and analysis, and gave counter examples that invalidate the main result. My advisor seem to agree with the errors during one of our meetings, but as far as I can tell no further actions were taken on the authors side. I then did not bring this up as I did not feel that was a good idea, since my advisor said I should "move forward instead of find mistakes in the past". However several months later my advisor is still endorsing the paper, and after I pointed out the errors again I received no reply.
So my questions are:
What should I do regarding this paper? Should I let this slide, or is there some higher authority I should report this?
What should I do moving forward with my Ph.D. studies? Does this event indicate the incompetency of my advisor? I know a suggestion might be switch advisors, but I've already tried working with several faculty members and the experiences are all none-the-better, and this has already taken a huge amount of time and I'm already several years into the program.