There are several things I can think of to monitor via Social Media. Most include what your top competitors are doing. For Top competitors and your company, I would monitor:
For your overall industry, I would track things like:
It's important to not only track your company but your competitors to gauge where you are at compared to them.
This is a lot to monitor but I have found that a few Google Alerts (or similar) do the job nicely.
There are various tools I use Ubervu for URL monitoring and Tweetdeck for twitter both are free and are pretty good at monitoring what goes on out there.
With regards to what to monitor.
One possible list would be You company name
Your domain name + perma urls if you have some important ones.
Keywords that describe the business you are in or the kind of product you sell.
I would also monitor Competitors names
Domain names of competitors
Perhaps even names of individuals
It all depends on how much time and money you are prepared to spend.
There are also more professinal services like Lithium and if you are really serious you should be looking into SocialCRM software.
You want as much as you can, It's a huge pain to go there and manually try to keep track of stuff so make them come to you by using:
Search keywords should be your company name,product name, URL and obviously usernames for social platforms such as @product_name (assuming you were smart and chose a good name that you can actually google and not a dictionary word )
I personally use tweetdeck as well to get instant results out of twitter, you can watch some keywords, quite useful stuff.