Usually all it does is changes the star from an outline to a coloured in star. That's all you'll see, but now people are notified that someone friended them, unless they removed it, I suppose... or maybe they're notified for both?
When you press CTRL+SHIFT+J (Chrome) or CTRL+SHIFT+K (Firefox), are there any errors when you click the button? And in the network panel, are there any errors there, either?
Also, when you friend or unfriend someone, the other person gets a notification, unless you friend them and unfriend them before they see the first one.