The real problem created by fan fiction is that, at its core, it is not copying of the work. At most, it involves detailed allusions to parts of the work. The copyright concept of "derivative works" is sometimes relevant here, but I question whether it applies (let alone should) in the context of telling new stories in somebody else's sandbox. (Aside: Many experienced writers refer to works that are based on someone else's material for more than just inspiration as "playing in somebody else's sandbox." I can't tell you the parameters of a sandbox—but I know one when I see it.) These are sometimes treated as more than just "fan efforts"; consider the controversy a few years back over Lo's Diary, and The Wind Done Gone. The real problem is that the Copyright Act does not establish standards for how much one can take, or who judges it, or when, or anything else. Instead, we're stuck with dubious judicial determinations, often overlapping the 1909 Act and the 1976 Act and based upon behemoths who can afford to litigate to death and their various interests—interests seldom consistent with those of smaller creators, or their fans.
Fan fiction functions through allusion. The allusions need to be detailed and "authentic"; giving Captain Kirk a propensity for Black Power salutes, a half-open shirt showing a gold medallion and lots of chest hair, and a fondness for early funk isn't going very far—and that's clear before considering good taste! Fan fiction can also create converse problems. There has been more than one instance in which a later-published work by an "authorized" creator was accused of infringing upon material from fan fiction. Some creators and authors dislike fan fiction for precisely that reason: They fear that their own work will be cabinned by what the fans do, including potentially closing off already-contemplated developments. (Remember, a great deal of fan fiction is inspired by ongoing serial works.)
More importantly, though, the allusions must be recognizable. Even when not understood as doing so by the authors, fan fiction must invoke a sense of being in that other person's sandbox, or at least containing a couple buckets of sand from that sandbox. Some fan fiction tries to make clear that it is not authorized by the creator; most is not so considerate. The real problem is not confusion by those who write fan fiction, though; most of them know perfectly well that anything appearing in their usual haunts—whether the hectographed fanzines of the sixties or the massive website repositories of today—is not "official," or the real (Dr) McCoy. The problem becomes most apparent when dealing with new fans who have had little or no prior exposure to the world of fan fiction, and don't know its cultural idiosyncracies (or even the idiosyncracies of their own little area).
So, then, is there an area of law that is tailored to allusions to specific sources? Can I write obvious rhetorical questions?