Mentioning other people's error in talk 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?
First, make double sure that the error is on their part, not your part, or there is not another reason for the discrepancy (e.g., they're computing something slightly different, they're using different assumptions, there's a simple way to transform their answer into yours, etc).
It seems reasonable sometime between now and then, to contact the authors (1 and 2), to check in and say you want to mention their work in your talk but you're concerned about this possible error.
Try to talk to Author 2 at the conference before your talk about this issue.
What to actually say depends on the situation and exactly how related their work is to yours, but if you are not getting any responses from them, you might just mention their work in passing.  You could avoid saying anything definitive about their work.  You can also just say that there seem to be discrepancies in some cases and you're looking into it.  I would avoid directly saying their work has errors unless they specifically admit that it does (in which case you still should not harp on it).