This is a long-shot, as I can't think of any way you can stop such scams, but...
Is there anything I can do about scam job postings[1] being posted on various free-ads sites online, claiming to be from the company I work for, and giving an email address at yahoo or gmail or some such? If I can get full email headers then I can get the email accounts closed at the various free providers, but this is just a game of whack-a-mole which will go on forever.
What else can I do (if anything)? This clearly isn't good for the company name, and given the current economic situation there are a lot of people who will reply to a "job" which says they can get easy money. And, of course, being the sysadmin you're put with the task of somehow stopping these fake job postings giving people the wrong idea about your company...
[1] Looks like cheque/check fraud, getting you to pay it in and then transfer the non-existent money to elsewhere. Then it gets reversed and you're massively out of pocket.
You're pretty much going to have to play whack-a-mole, but this is where the DMCA is your friend. Every time you find a fake ad, if they are using any of your images, you can send a DMCA take down notice to the job site running the ad, claiming copyright infringement. Generally, companies that take user input have a fast-track for DMCA notices, so this might be more effective than just asking.
As a matter of fact, oftentimes the scammer will be lazy, and just hotlink your logo right off your site. So you can actually check your referrer logs to find these scam posts sometimes.
In a word, no. It would be nice to have some way of monitoring this so that you can get the posts/emails removed but it is so easy now to put fake information on the internet and get away with it.
But if you do think of a way to do it, I'm sure you could market the idea and make a fortune out of it. Good luck ^_^