First, I'm not fan of Campbell (see the excerpt below); I believe he is attempting to address the fact that values were changing so rapidly in the post-modern industrial world that what had been acceptable - prejudice against certain groups of people, for example - was no longer acceptable. Without a broader context, it's hard to say what he is saying.

Here is an excerpt from my Introduction to Folklore, a section dealing with Campbell; perhaps it will help put his work in context:

The popularity of one particular approach among non-folklorists warrants a digression. In the last part of the twentieth century, Joseph Campbell (1904-1987) created a great deal of interest in mythology and folklore with a series of publications on the subject. This was followed by a 1980s series of television interviews, which propelled Campbell to popularity with the general public, but not necessarily with all folklorists. To a certain extent, Campbell was relying on an older approach that Carl Gustav Jung (1875-1961) developed. Jung was a Swiss psychologist who studied with Sigmund Freud (1856-1939) but later broke with his mentor’s teachings to form his own approach to the study of the human mind. Jung developed the idea of the collective unconscious, maintaining in almost spiritual terms that all of humanity is linked by archetypes that existed in an unconscious common denominator. Ultimately, Jung implied that certain themes are woven into the fabric of the universe. This results, according to Jung, in a shared symbolic vocabulary which manifests in dreams, mythology, folklore, and literature.

Jungian psychology was extremely popular during the upheavals of the 1960s when people looked for mystical explanations of life to unify all existence. In spite of the faddish qualities of the late twentieth-century consumption of Jungian ideas, it is easy to regard Jung as an exceptional thinker with an extraordinary background of diverse reading. Campbell borrowed heavily from Jung, presenting many of these ideas in an easily consumable package that, in its turn, became something of a fad during the 1980s. Campbell drew not only on Jung, but also on Otto Rank’s 1932 publication, The Myth of the Birth of the Hero.

There are clearly many good ideas in this literature, but there are problems with the approach of Campbell, Jung, and Rank from the point of view of folklore studies. The first is that they tend to present the concept of tale types in mythology and folklore as though it were a new discovery. In other words, they ignore the highly developed bibliography that the discipline of folklore offers. The second, more serious problem is that this line scholarship makes no distinction between the core of a story and its culturally-specific or narrator-specific variants and variations. The Jungian-Campbell approach treats any variant of a story as an expression of the collective unconscious, regardless of whether its particular form is the product of an individual storyteller’s idiosyncrasies or of the cultural predilections of a region made irrelevant by traveling to the next valley. And with this process, all the other variants are ignored, including ones that may contradict the initial observation. This does not mean that there are no valuable insights in the work of Jung and Campbell. There are, of course, but folklorists regard their approach as removed from their own discipline and flawed, to a certain extent.

Dundes presented a similar critique of Freudian-based psychoanalysis of folktales. In his The Study of Folklore (1965), he wrote that “the analysis is usually based upon only one version…To comparative folklorists who are accustomed to examining hundreds of versions of a folktale or folksong before arriving at even a tentative conclusion, this apparent cavalier approach to folklore goes very much against the grain. How does the analyst know, for example, whether or not the particular version he is using is typical and representative.” (107) Dundes also pointed out that often the “variant” presented by the psychological analysis is from “a children’s literature anthology, rather than directly from oral tradition.”

There was also a wave of pop-psychological treatments of folklore, arguing, for example, that the material is sexist in a variety of ways or that it can be transformed to provide young girls with a positive self-image. It should come as no surprise that peasant folklore from the nineteenth-century was sexist since it came from a male-dominated society. On the other hand, there is a long-held practice of re-writing folktales to suit the needs of the moment. That is exactly what the Brothers Grimm did in their effort to provide speakers of German with a national, popular literature. If there is gain to be had by feminizing folktales, the effort can take its place in an honorable tradition.

I actually asked a similar question to this with very fruitful answers in /r/askanthropology, which I unfortunately am not able to locate. I'll try to summarize what I learned from that discussion as well as what I've since gone on to read.

The problems you should be aware of with Joseph Campbell revolve around his attempts to universalize both the symbols and the meanings of myths around the world into what he called a "monomyth", or said in another way, the "hero's quest." However, he had a tendency to cherry pick anthropological data specifically in order to create the illusion of a universality to myths and meanings.

What anthropology actually has shown instead is that while the symbols/signs of a myth may share a commonality (a man sacrifices himself for his family) the meaning of it is arbitrarily and culturally defined (was that a good or bad thing?). A random example off the top of my head would be Christopher Columbus set sail across the ocean and landed in America. What does that mean? Was it a good or bad thing? Obviously Native Americans would look at that event very differently from Europeans, and methods of constructing "positive" or "negative" meaning from that symbol/event are dependent upon arbitrary framing, i.e. positive/negative to who and across what time frame?

So the issues that I presume people would have with Campbell, is that he believes (and thus creates) a position from which all myths have universal meaning (which conveniently tends to be his interpreted meaning) and that society must take these meanings as models for behavior.

Which in the face of post-modern understandings of meaning as inherently "slippery", makes Campbell seem quite inflexibly dogmatic as to demand only one meaning (which once again, conveniently happens to be his).

For more information though, I would strongly recommend also posting yourself to /r/askanthropology. Tis a good sub.