In SCII you can right click on a friends name and "set friend note". What is this? What does it do? It allows you to type in text but nothing happens after you save it. So is this for your reference?
The set friend note is for your own personal reference, you can type anything in there that you want.
For example, if they are not your RealID friends with them and just in game friends, you can set a note to remind you that Sorean is really Neo Matrix. Or you can say put into the notes that I play protoss and enjoy adding Dark Templar's into my late game play.
I'm not sure why it's not saving anything for you, but it is working and saving the notes I typed for anyone on my list.