Kida has a useful list of characteristics of pseudoscientific thinking:

There are varying degrees and causes of pseudoscientific claims. Sometimes there are honest mistakes; other times, they are less honest. For example, people can often see images in random patterns (pareidolia) or make connections that aren't supported by clear causation or logic (apophenia): these are simply manifestations of the fact that the human mind is sometimes confused. Also, we can be honest victims of other people's dishonesty.

A harmless case of mistaken observation: reports on 31 July 2008 stated the following:

Subsequent footage from video footage from near the Arena Drive Garage revealed that the cat in question turned out to be a savannah cat, a hybrid of domestic cat and the African serval. So it wasn't a wild animal, but someone's thousands-of-dollars pet! (So far as I know, the cat was never captured.)

In this case, an extraordinary claim was quickly overturned by additional evidence, and that evidence was quickly conveyed to the public. The problem is that this is not always so, and because of this pseudoscientific claims can thrive.

For example, the claims that a rotting plesiosaur carcass was found by a Japanese fishing vessel in 1977 continue to be made, even though it was established in 1978 that it was just the remains of a dead basking shark! The media widely reported the "dead plesiosaur" hypothesis, but did not follow up on the results of the investigations that showed a much less exciting answer.

Even when a claim is strongly falsfied, there are some "true believers" who refuse to give them up. A classic case is the "Face on Mars". As the Viking Orbiters gave us some of our first good photographs of the surface of Mars, they caught an unusual image in the region of Cydonia Mensae:

Notice how through a trick of lighting & shadow (and some well-placed coincidental pixel dropouts) one of the mountains looks like a human face, with vaugely Egyptian headgear:

This image drove the UFOlogists, Ancient Astronaut fans, and others into a frenzy: Proof of Human-Like Martians! Even when much better pictures were taken of the mountain by more advanced probes launched in the 1990s and 2000s, such as:

that clearly show it isn't a face, the supporters of the Face-claim do not back down.

Pseudoscience can be promoted for financial reasons. Pulp science fiction magazine publisher Ray Palmer (of Amazing Stories) ran a series of letters by Richard Shaver in the 1940s. Shaver claimed that during WWII he had wandered into the Hollow Earth, which was populated by four-foot tall bald grey deranged robots called "deros", who flew around in disk-shaped ships, caputered people, probed them, and released them with mind-controlling implants. Shaver's letters caused Amazing Stories' sales to soar, and others began to write in about their own similar experiences!

In Spring 1948 Palmer (under the pseudonym "Robert N. Webster") started publising Fate magazine, dedicated to the "Shaver Mystery" and similar paranormal tales. The feature article of issue one was the story of Kenneth Arnold and the "flying saucers" (see Sagan Chapter 4).

The popularity of Fate led to many similar magazines: some professionally produced, others privately made "fanzines". At least some of the latter were actually created as hoaxes. Gray Barker, head of Saucerian Publications and known UFO photo hoaxer, invented the "Men In Black" in his 1956 book They Knew Too Much About Flying Saucers. More recent hoaxers that created entirely new pseudoscience legends include crop circles and Charles Berlitz's Philadelphia Experiment and revivals and retroconditioning of the Atlantis story and of the Roswell Incident.

A famous pseudoscience movement of the 20th Century was the Ancient Astronaut hypothesis. It claimed that the legends of ancient people interacting with heroes and gods who taught them skills and knowledge were actually a partial record of encounters with aliens. As archaeologist Kenneth Feder points out, Ancient Astronaut proposer Erich von Daniken suggests that alien knowledge was necessary for building numerous structures throughout history in Africa, Asia, and the Americas, but doesn't suggest that the people of Europe needed alien technology or skills to do their own contemporary buildings.

Some patterns of pseudoscience:

We've seen some cases of pseudoscientific claims that are basically benign ("all in good fun, so what's the harm"). But it isn't always that way...

Pseudoscientists can often be benign, but their lack of critical thinking has in the past allowed unscrupulous people and movements to take advantage of them. For example, Adolph Hitler's rise to power in Germany is at least in part due to pseudoscientific movements of the early 20th Century:

Within cultures like the Third Reich, the USSR, and other oppressive authoritarian regimes, pseudoscience could flourish for a variety of reasons:

Germany in the early 20th Century had a very well-educated public and was on the cutting edge of many lines of scientific and technical research. Nevertheless, in Nazi Germany many types of pseudoscience flourished alongside real science and technology. In the realm of the Earth sciences, bizarre notions of a Hollow Earth or the World-Ice-Theory found official support.

After the end of the war, legends quickly developed about the possible survival of Hitler and some of his cronies. Among the more bizarre claims were that he may have fled to a secret base in Antarctica, or in the Hollow Earth, or off to the Moon!

Here is a recent essay about 7 Famous Unsolved Mysteries Science Solved Years Ago.