I know a student was harassed last year and decided not to complain in any formal way. What, if anything, should professors and departments do when they know something was (still is?) a problem?
Note: You say that you KNOW harassment has taken place. I am, then, assuming for the sake of my reply that you really do have sufficient evidence to be confident of this.
There are a lot of unclarities about your situation, and they are ones which matter. You haven’t said how severe the harassment is. From everything you say, it might well be fairly low level casual comments, best dealt with by a bit of collective consciousness raising. One way to do this might be for someone in a position authority to make it clear what sorts of comments are and aren’t appropriate, and to urge on everyone else that they have a duty as bystanders to speak up when inappropriate behavior takes place. Ideally, this could be accompanied by department-wide active bystander training (<http://web.mit.edu/ombuds/publications/bystander.pdf>).
You also don’t make it clear whether the source of the harassment is students or faculty. All of the same strategies are appropriate to lower-level harassment in either case, but with graduate students you should consider the additional fact that part of what you are meant to be teaching them is how to be a member of the profession. Training on appropriate behavior is a crucial part of that, and everyone should be considering incorporating that into their graduate training program, whether or not they have had problems (yet).
But if the harassment is more severe, this sort of consciousness raising is likely not to be enough, and indeed you are likely to be legally obligated to do more. Since you are at a US university, it is very likely that you actually have a legal responsibility to report the harassment to your university, though you may want to confirm this with legal experts. (Importantly, it is not only victims who are able to make complaints.) Before you do this, though, you need to think hard about ways to make sure that the student is sufficiently protected.
Whether or not you have a legal obligation to make a complaint, you should not limit the actions that you consider to formal ones. (Not all the strategies suggested below are appropriate to all situations– they are present as a menu of options.) You should also consider:
1. Confronting the harasser about his (I’m assuming) behavior, getting a group of people together to confront the harasser, or getting your chair to do so.
2. Getting the chair to make a public statement about acceptable and unacceptable behavior.
3. Working with your chair to minimise the chances for this person to do further harm.
4. Getting training for the department on sexual harassment, and also on active bystander strategies.
5. Making sure that the victim is getting the support that she (I’m assuming) needs, including protection from retaliation, and if necessary help in securing new mentors.
Finally, whatever the situation, I’d urge your department to sign up for the APA’s site visit program. This will allow them to get expert advice on ways of improving the climate, tailored to the problems that exist in the department.
At my institution at least faculty are obligated by policy to report any such incident. But more importantly, I think we need to foster a climate in which it is not an option for a student not to report. When such a student appears in my office, I take her by the hand and walk her to the appropriate reporting person. Then I sit with her as the reporting person and she hash things out. Harassment only stops when people call it out, loudly and clearly, for what it is. Students need reinforcement that this behavior is flatly unacceptable, and that it is okay to complain about it, and they look to us to give us that reinforcement.