Anonymous Student Feedback: Moving forward from abusive comments

It sounds like you've encountered the well-known downside of online disinhibition effect, more colloquially known as GIFT. There is simply nothing that can be done to prevent some people from being horrible when offered anonymity.

So, let's parse out two different questions about how you should react: 1) what actions should you take to protect yourself and other students? and 2) should you continue to use the anonymous feedback form?

Let's start with the first question: given that you know there is a horrible person in your class, what should you do to protect yourself and other students? I see three basic possibilities here, either a) the person is insincere in their statements and is trolling you to try to get a reaction, or b) the person is genuine but not a threat, or c) the person is an actual threat to the safety of yourself or others. If you are concerned that it might possibility c), then if there is any way for your IT staff to penetrate the anonymity and investigate, it's reasonable to ask them to do so, just as if somebody had made a serious electronic threat through some other channel (your institutions likely will have a process for reporting serious threats of harm, though, which may mean you shouldn't start by going directly to IT). Otherwise, it's probably best to ignore it and move on, because otherwise you're just giving them the reaction and power over your actions that they are looking for.

Now, turning to the second: should you continue to use the anonymous feedback form? The one problem with true anonymity is that if you get more nasty comments, you can't tell whether they came from the same person or not. I would recommend looking into whether you can get pseudonymous information from your system, i.e., so that Student X's comments are all collected together and Student Y's comments are all collected together separately. That way, you can separate out and discard feedback from the horrible person (essentially marking them with a "troll" filter), while still getting meaningful feedback from other students who have more positive disinhibition from the anonymity.

It's a pity that some people are horrible and try to screw things up for everybody else; the rest of us need to try to figure out how to appropriately protect ourselves and our institutions while keeping them from profiting from this behavior.

You must die! You're so cool! These are, at the two ends of the spectrum, example comments that I have received from students along the years.

You will find students who love you, those who like you, those for whom you are indifferent, those who dislike you, and those who plainly hate you. This regardless of what you do as a teacher, that is, even from week one of the class.

Those who love you will deliver overly enthusiastic comments; those who hate you, protected by the anonimity, will insult you in the worst possible ways and will wish you all sort of bad things.

My advice is: don't be too pleased by the former, and don't get sinked by the latter. In particular, for what concerns the abusive comments, unless they hide a real threat, brush them off and move on.

A short answer, but I believe that it answers your question:

Threats of violence correlate with, but don't cause, violence. As such, eliminating the medium that enabled that student to anonymously communicate threats of violence, as you have proposed to do, does not reduce the probability that one of them will act violently. However, it does ensure that no student can anonymously communicate useful insights about the course to you.