One of Logitech's best wireless products was their Logitech ClearChat. From an audio quality perspective that it. It's manufacturing quality was disastrous, and the internet is filled with people complaining about issues with their microphone (turning silent, not turning on, turning off when you move year head).
Just very annoying to use when the microphone breaks down.
Got a different product today the Logitech H600 (there don't seem to be many manufacturers of wireless headsets). Didn't work straight out the box with Ubuntu. I.e. it turned up immediately, but there was no sound. This appeared to be a communication problem with the wireless receiver and the headset.
bhankins found a solution that works for me too. Download the pairing utility and that fixes the problems. Unfortunately the pairing utility only works on Windows (or perhaps wine, didn't try that).
Hopefully my microphone problems are now solved. But sound quality is definitely much lower than the ClearChat, but won't matter for Skype/phone calls I'm guessing.