First off, I'm entirely against a firearm in this incident. It's far more likely to be used improperly under the circumstances than anything else. Some type of non-lethal, incapacitating item will more than suffice. I am leaning toward pepper spray of some kind and every time she enters or leaves the area, she should have it at the ready. It's far less likely to cause the type of destruction that a weapon of any other kind would if employed against the wrong target. Plus, you've all but said that she's afraid of them and you don't seem to have a lot of experience with them, much less acquiring and firing on a moving target at night and considering your backdrop (ie.-the person in their living room in the adjacent building) and the other factors that come with years of experience with a handgun.
Second, lighting is key. Guys like this love hiding in the shadows to conduct their business. Hell, buy her a 10,000 candle power spotlight to use to check the area at night if she's that bothered by it, which she certainly should be somewhat concerned about it. A thorough analysis of the lighting situation in the complex and especially in her immediate areas should be conducted. Any lights you notice that are not functional or burnt out should be reported immediately to the grounds keepers for replacement.
Third, don't hesitate to call the police and request increased patrols in the area if this hasn't been done already. At those times of night, most cops are happy to be able to turn on the spot lamps and alley lights on their car or get out and question people in the area who shouldn't be there. Believe it or not, a large number of criminals are caught doing seemingly harmless things like this.
Finally, train her to be fully aware of her surroundings. I teach my wife everything I can to defend herself. I'm not talking years of martial arts training either. Things like turning on her high beams coming into the parking lot and giving a good visual scan of the entire area before pulling in. Keeping her door locked until she's ready to get out of the car. Practice making use of the Panic feature on her keyless entry remote if it's equipped with it. Approaching corners by walking out and around them to give you reaction time should someone be waiting to ambush you. All of these things any many more can prove effective if simply practiced and thought about and none of them will really make her seem "paranoid" as many women often end up feeling doing things like this. It's not like you're teaching her to combat roll around the apartment complex or camo up her face before going out.
I hope these things give you something to think about, discuss and act upon for this incident.
PS-we worked for the better part of 3 weeks two summers ago to catch a peeping tom and never did. Fortunately, nothing ever came of it in the way of violent crime or anything, but it was very annoying to always be one step behind the guy.
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