I too have to add my voice to this thread. I hadn't realised there was a problem until I bought a set of ultimate ears 600vi's this week. They were bought specifically for use when driving so I could lower the headset volume compared to the basic apple headphones as I found I had to turn these up so loud to get over the road noise I got tinnitus!
I immediately noticed that during the phone call I heard my own voice through the headset and also the background road noise. When the call stopped, the background noise stopped. This amplified background noise is such that it often drowns out the person on the other end of the call. I thought it was a faulty headset but then stumbled across this forum. I have since been experimenting & the problem occurs with both the ultimate ears and the standard apple headset and is reproducible every time. It does not happen when either headset is plugged into my old 3GS.
I agree with other posters that this only happens in the phone app. It does not occur when talking to Siri, or making facetime/skype/viber calls (over wifi or 3G).
The phone app seems to be taking the audio signal from the microphone, feeding it to the network (since the person on the other end can hear you), but then also pumping it back to the headphones. This is easily proved by rubbing your finger over the microphone during a phone call (you'll hear the scratching in your own earphones) compared to during a facetime/skype/viber call (you won't hear any scratching). If you have an "in-ear" headset, place one of the earbuds next to the microphone during a call - you'll get the classic high pitched feedback loop in the other earbud (this doesn't work with the stock apple set, presumably because the speaker isn't as good).
Surely this is a software coding glitch if it only happens in the phone app?
It could be argued that this constitutes a health and safety issue as the problem increases the dB levels experienced when using a headset, with the associated detrimental effect on long term hearing.
If you're listening Apple, you need to fix this.