My sister and I are having the same problem you all are encountering. We have the new iPhone 4S 64GB and are with Rogers. We actually went to Apple store yesterday and got new phones, however we still have the problem. We don't know what to think, it would make sense that it is a hardware issue, however it seems to be a limited problem (in that there isn't a massive reporting on the issue, lots of message boards talking about it etc.). We wonder if it is carrier related, somehow... we just don't know.
My sister restored her phone to factory settings and used it and still had the problem. We've tried restoring, resetting the network, nothing works (other than unplugging the hands-free set). It seems there was the same issue with the iPhone 4 when it came out. There are some older threads on this, but I don't know what the final resolution was to the problem. The postings on it seemed to stop, so maybe it cleared up? No idea.
For samchr, the problem presents as the other person hearing an echo. So, if you are speaking with your wife and she hears the echo, then it is your phone, and vice versa. As my sister and I speak to each other on our new iPhones we've worked it out. Another way to check is to unplug the hands-free set and see if the problem goes away. Which ever one of you clears up the problem by unplugging the hands-free, that's the phone that is causing the issue.
The problem is sporadic, it makes it harder to diagnose. I was out walking and had a fairly long phone conversation (12 minutes) with no issues. On the phone with my sister yesterday, it happened about 8-9 minutes into the phone call (I believe, I didn't check). Today I was speaking with my sister for just a short time, and the problem happened, but on her end this time.
It's a real puzzle. If anyone finds out anything on this, PLEASE post the solution for us on this board!