Hi
I have the Logitech Headset Premium Stereo 350 USB. Since the 10.4.6 upgrade (I think) it has not been working as it should, but it does still work. You need to go into System Preference > Sound > Output, have the headset selected as the output device, and then click the mute button on and off. Have the headset on while you do this and play with the volume control at the same time so you will hear when the sound does start to come from the headset. I have no idea why Logitech have not sorted this problem out yet, but the headset does work fine if you are prepared to fiddle around every time you use it.
While we are here I want to recommend
SoundSource for quickly changing audio inputs and outputs. It doesn't help much with the current problem, however.
Edit: BTW on my headset, the flashing blue light is the mute indicator for the microphone. Pressing the centre button toggles it on and off.
Matthew Whiting