As I do with any new product in the social space -- I have been using, analyzing, and testing Google+ since it came out (on top of that I'm pretty sure I invited at least half of their initial user base... give or take). After using it for a couple of weeks, here are three product suggestions I have that would help with the Google+signal to noise ratio. Hit me up on Twitter @MattPRD if you want to discuss any of the ideas in this article or the social web in general.
If you like any of these ideas send out a Tweet or give this article a +1.
Recommend Circles I Should Share To
When I share content, Google+ should auto detect what the content is about, determine which of my circles are likely to care about it and then recommend that I share to those circles. With the ability to add Recommended Circles with one click I would share targeted content on a regular basis.
Targeting content appropriately is important because everyone that wants content from me doesn't necessarily care about everything I say. Some may want to hear my thoughts on Social and Product where others may want to only hear about my thoughts on San Francisco restaurants. If I send everyone everything all the time people are going to get information that isn't always relevant or valuable to them -- where if I only send certain groups information based on what I know they want to hear then their newsfeed's become a lot more targeted and valuable.
Google+ could do this by matching the keywords in my status with keywords people from my circles use in their status updates or bio. My circles with the most matches would be recommended. Google+ could also check which people in my circles typically +1 or comment on content similar to the post I am attempting to publish and recommend my circles with the most matches.
Public Circles
Another way to improve targeting on Google+ is to have a public list of my circles (circles that I have chosen to make public) on my profile and allow people to add themselves to the circle(s) of their choice. This allows the user to choose what type of content they want from me instead of relying on the publisher (myself) to know this and hopefully put them in the right circle.
To encourage users to add themselves to Public Circles Google+ should integrate this flow:
A user adds me to one of their circles > Google+ shows them a list of Public Circles I have created > The user chooses which circles they would like to be in based on the type of content they would like to receive from me > The user is now in those circles and when I share to them they will see that content.
Friends in Hangouts Right Now
Google+ Hangouts is a fantastic product. I love that I can put out a public invite (or target a circle) and very quickly be video chatting with people from around the world. The problem is that if I haven't started the Hangout I need to rely on the feed to know if one of my friends is in one!
Google+ should show me a list of people in my circles that are in a Hangout right now. From a UI/layout perspective they could very easily add this to the right of Google+ home page in the "Hangouts" section. This would give active Hangouts more visibility and I would be likely to engage with them more often.