Problem:
Sometimes employees within a large company don’t really know what people are saying about them on the outside.
Solution:
Sure, most people know about the big news headlines on your company, but not everyone knows about all the little conversations and stories that spread.
So every once in a while (or on a regular basis) do a google or a twitter search for your company and find something interesting that people are saying. Then send a link to your group, or to people within the company who you think might care about that particular story or item. If there are entire internal communities on that subject, send the link to the email distribution list.
It might cause a stir if your company is misrepresented or some information is inaccurate, but that’s not really your purpose (unless you want it to be.) What this will do is make you known as someone who’s connected, who has the pulse on what’s happening on the outside. It might establish you as some kind of expert, or a ‘go to’ person in certain situations.
Sure, anyone can search google or twitter and find the same info, but the fact is they didn’t. You did. And you shared it with those who care.
So do it first and establish some credibility.
grootship 
>if your company is misrepresented or some information is inaccurate …
It’s Interesting to note that it will (probably) be the first reaction.
The point is that people outside of your company do not have the same vision as you do and this vision has it’s own value.
An exemple of this can be found here :
David Byrne is angry with me
http://sethgodin.typepad.com/seths_blog/2010/04/david-byrne-is-angry-with-me.html
You’re right, Didier. It definitely looks different from the outside than the inside.
And you can try to influence, but you can never control what people think.