Keepin' em crossed!
My DH had one of those co-workers a few years ago and he succeeded in getting him fired by saying he was slurring his words and then getting a "customer" report that to the owners (he had a very slight slur from one of the medications he was on). When it went up for review in front of the Workforce Commission, the owners came very close to saying he was let go for medical reasons (which is a protected status and if they had said that it was for medical reasons, my DH would have sued them).
I have an old boss that has been bad-mouthing me here - when I was up for another position here (as opposed to being let go for economic reasons), he bad-mouthed me and the person who was going to hire me told me about it and hired me anyways because this guy has a habit of bad-mouthing a lot of his ex-employees and has even gotten a couple of them fired. Probably why his department has a high attrition rate. Then I find out from one of his current employees that he got terrible reviews from all of his employees (yes, we get to review our bosses) and those reviews went to his boss. So I have a funny feeling his words no longer hold much credence.
I guess what I'm trying to say that even if the co-worker succeeds in bad-mouthing your DH, it might not work against him in the end. But I honestly wish the best of luck to him....