Where did this notion come from????
Some academics have big heads, but this is true in any field of endeavour. Academics tend to be highly educated by virtue of their job requirements, but they are as prone to normal human foibles as any other group. Most get into an academic career because of their love of research and/or teaching. Not because of some sort of expectation of God-like authority, for Pete's sake!!!! Regular faculty are subject to teaching evaluations by students, and these become part of their annual performance evaluations. When academics submit an article for double-blind peer reviewed scholarly publications, it won't get published if the referees point out serious flaws in the study. Academics often cut one another down to size, whether due to scholarly disputes or simple personal dislike. I could name further institutional checks on runaway egos, but you get the picture.
People known as "independent scholars" have long made serious contributions to knowledge. I would put in this category someone like astrologer Benjamin Dykes, who has translated a lot of astrology texts. Back in the 19th century, Charles Darwin worked from home and never held an academic appointment. Today, it depends upon the field.
It's hard to be an independent biochemist or molecular biologist, for example, because the average person can't just do this work in her basement the way Frankenstein could. Lab equipment is incredibly expensive. A typical well equipped lab today would cost a few hundred thousand dollars. Moreover, scientific research today is typically done in teams, not by the lone scientist at home.
Of course, a lot of science and social science research is conducted in government agencies and corporate research labs.
Moreover, a danger of independent scholarship in today's Internet era, is that some independents attempt to sidestep the rigorous peer review process and public debate to which academic research is routinely subjected. This isn't true of all independent scholars by any means (notably in fields with far more applicants than job openings, where many highly qualified applicants can't get hired,) but sometimes scholars cannot get hired because their research just wasn't that exceptional. Once they are out of the loop for 8 or so years, it is hard to get back in because they haven't amassed the c.v.
Even with a field like translation and editing a critical edition of an astrology text, the scholar may still need to travel to archives because scarce and fragile manuscripts cannot just be checked out of the library, and all this costs money.
One thing about "mistaken" academics, however: knowledge is a cumulative process. It is also often subjected to the criterion of duplicability. Theories are based upon the "best fit" with the available data. When more or different data become available, then the theory may have to be modified or even replaced to explain the new data. Continental drift is one classic example: It was talked about for decades, yet its acceptance had to await more advanced knowledge of plate tectonics.
A classic source on the problem of knowledge accumulation in science was Thomas Kuhn,
The Structure of Scientific Revolutions.
http://plato.stanford.edu/entries/thomas-kuhn/
Or sometimes a team of scientists will publish a finding, together with the mandatory methodology section of the scholarly article. If the topic is sufficiently intriguing and novel, other scientists will probably try to replicate the findings. If they can't, then the initial article is seriously called into question.
So it's a bit odd to say that "academics are often wrong," without understanding the process through which knowledge gets incorporated, tested, and sometimes replaced.
But I will tell you where both academics and independent scholars "are often wrong." It is on topics where, although they may have a strong background in one discipline, they purport to dispense wisdom about another field in which their background is inadequate.
Academics don't criticize fringe theorists like Velikovsky,
von Däniken, or Stichin because they aren't or weren't In With The (Academic) In-Crowd. Academics criticize them because their work doesn't stand up to rigorous scrutiny.
There is a credible field called archaeoastronomy. If Herschel's work can stand up to scrutiny from experts in this field, more power to him. I googled him and could find no biographical information or analysis of his work on line.
https://en.wikipedia.org/wiki/Archaeoastronomy