I got the green blinking light, and my mouse would not connect. I tried three different sets of batteries and all three just made the mouse blink twice over and over.
I deleted my apple mouse as a recognizable device from my bluetooth preferences, as someone else suggested. However the green light was still blinking and my bluetooth couldn't find my mouse to reconnect it. Then I clicked "turn bluetooth off" and then turned it right back on - and bingo! It saw my mouse, I re-paired the mouse, and all is good!