To start with, archaeology is the analysis of physical remains, paying special attention to the context of those remains — their geographic location, location relative to other items and within the strata of the region, any documented historical context, and so on. Further, he stated that there is an assumption among archaeologists that other archaeologists are interested in the best explanation for things.
Pseudoarchaeology — "armchair archaeology" if you will — is performed by people who are not interested in the best explanation at all. Rather, the goal is to attain sensational results — and as such, truth that inconveniently gets in the way of that goal is ignored, denied, or derided as being part of a conspiratorial establishment. It abuses select methods of archaeology for the purpose of lending credence to itself. So, for instance, it may take a small piece of data and fabricate a vast conclusion from it. Or it may rely on outdated models — cherry-picking debunked theories to support a hypothesis.
The thought then is, "so what?: legitimate archaeology will debunk their findings". Well it's not so hard when some guy shows up on TV with a wrench and claims it's the bone of a metal dinosaur. But when it's someone who's published a dozen books under the "archaeology" category, it's quite another.
And therein lies the cornerstone for the "dangers" that Dr. Fagan outlined. The pseudoarchaeologist makes their conclusions first then finds data to fit that — specifically, they skip the peer-review process that is designed to strengthen legitimate theories and diminish illegitimate ones. Relatedly, they will deride critics and celebrate supporters; whereas a true archaeologist will celebrate the respectability of criticism or support and deride inferiority. Frequently the pseudoarchaeologist will leverage nationalism and other unrelated reasons affect objective investigation.
But worst of all is that these pseudoarchaeologists don't do any real archaeology but they are supported under false pretenses to establish dig-sites which are no more respectable than (and just as destructive as) looters.
The key — in my mind — is that the average person is not an expert in archaeology (and in point of fact, is seldom an expert in any more than one field). As such, they rely on indicators of expertise to make a decision: advanced degrees, validation from others, longevity of their claimed expertise, etc. Unfortunately, all of these can be forged and the non-expert is left wondering what to do.
I guess for most, it's to remain vigilant. Look for telltale signs — sweeping conclusions, derision of all critics and celebration of all supporters, and a strong influence of motivations external to the work-at-hand.
I also left the lecture with a sense of familiarity for the kind of person that makes a pseudoarchaeologist. It's the same traits that make up the pseudoscientist and the fraudulent leader. In all these cases, the perpetrator of fraud creates an environment of power and prestige by convincing people that established knowledge is simply a conspiracy against wonders-untold that is otherwise claimed untrue.
For the pseudoarchaeologist, it may be that ancient civilizations were far more advanced than we are — despite established knowledge that they used tools and techniques that we have built upon to become more advanced than they. For the pseudoscientist, it is almost exclusively an attack on good old Thermodynamics Law #2: that you can't get more energy out of something than you put in — perpetual motion machines, and miraculous energy machines constitute the bulk of their exploration. And for the fraudulent leader, it is a claim that vast improvements can come from their method of leadership which history has consistently shown to be a path to a civilization's destruction.
And I agree with Dr. Fagan's comment that these people are not evil, just misguided. They are often deluded by the same thing that tricks others: the fundamental belief that great rewards exist to be claimed; and the refusal to accept that sometimes the greatness of a reward is distorted to be larger than it actually is when observed from afar.