I am a 3rd-year computer science PhD student and I have recently written and submitted a paper to a theoretical conference. It has been accepted; but the reviews were not very in-depth. Usually they were of the form: "I didn't check the proofs but the statement sounds reasonable."
Now I have to say that we work on a very complicated topic in which there are maybe just a few experts worldwide; and even for those it would have probably taken them a few weeks if they were to check the proofs in depth. In light of this I was not very surprised that most of them just took a quick glance.
While preparing the presentation, however, I myself noticed a mistake which is not easily solvable. I did find a solution, however, that keeps the main proof structure intact, but one of the main definitions has to be changed.
I asked my professor what we should do about the paper, and he said to leave it be and publish the corrected version in a journal later. However, I still feel kind of uneasy pretending as if nothing happened. What would be the ethical approach? I realize that it is probably not possible to "stop the presses", but should I notify the conference organizers about it in any way? Or should I mention it in my talk?