I really love the idea. I totally agree that sometimes you want a camera always filming everything to capture the instants, because when you take your phone out it's already too late and you can't really reenact it. That's a good thing.
What I, and I believe others didn't like, is the text and the message, which is not even hidden at this point: Google sees and knows everything about you, your family, your favorite moments. I didn't even see how that was useful for the user -- I certainly want to categorize my Moments so I can easily find them again, but I'm not sure I want Google to _know_ about it. And yet that's exactly what it says.