I am a PhD student of physical chemistry, and my work involves developing packages for numerical simulation. Recently I tried to reproduce some work done with a rather well known package made by a (friendly) competing group, and failed. After some time, I found out that the discrepancy was due to an error on their part.
I asked my supervisor, and she suggested that I should write the authors. The corresponding author said the result was due to Author 2, a rather well known and respected senior of my field, and that he would get in touch. It has now been over a month, and I have heard nothing. I am still convinced that their result is wrong. I am hesitant to write back, as I don't want to appear nagging.
Here comes the tricky part. I have been invited to give a talk at a conference in June. The conference is a rather high profile thing in the US, and lots a possible future employers will be there to hear the talk. And, as I have seen from the participant list, also Author 2. It will be strange if I don't mention that his software package is capable of doing the same calculation as I do, as part of my invitation involves giving a small review of the sub-field. But if I do, I will have to say that they do it wrong. I don't want my talk to become argumentative about a mis-calculation, as I want to make a good impression on a lot of people.
How do I gracefully talk about our work, without this turning into something ugly?