The Japanese hypergrowth of the 1970s and '80s was built on a system of buddy-buddy relationships between various corporations and the government. At the time, this system appeared to be a triumph of modern corporations and state-directed capitalism, but nowadays, we just call it "crony capitalism". Predictably, this created an unsustainable economy based on *ahem* loose credit, a housing bubble, selling below profit, and toxic loans. Property values became massively overinflated, to the point where prime real-estate in Tokyo could sell for more than the entire GDP of smaller countries. At the height of the property bubble, office space in Tokyo's main business district went for a million dollars per square meter∞ ; land in the Ginza shopping district cost ¥30,000,000 per square meternote ; and the value of the Imperial Palace was greater than all the real estate in California.
This, and the appreciation of the yen by mid-80s started a Japanese buying spree of American properties such as Firestone Tire and Rubber Co., Columbia Pictures, and the Rockefeller Center, prompting feelings of insecurity especially in America, where Japan was often still remembered as an old foe.
But once the bubble popped, the economy stagnated, and Japan entered a "lost decade," and some say it still hasn't completely recovered almost 30 years later. Banks became zombie institutions, the central bank got stuck in a liquidity trap, and Japanese twenty-somethings faced a fate worse than death while their fathers had enjoyed lifetime employment at one company, they moved from temp job to temp job, failing to build much in the way of careers. In short, they weren't half as inhuman as the mythos.
A major factor in Japan's boom was the necessity of rebuilding all the infrastructure after World War II. While a burden in the 1950s and '60s, by the '70s the Japanese economy was enjoying the benefits of much newer, more modern factories than the United States (a similar situation happened in Europe, particularly in West Germany, but the Cold War was more of a factor there). Also, the West put quite a bit of investment into the reconstruction of post-war Japan, particularly during the Allied occupation and the decades that followed. They also got help from W. Edwards Deming, who had been responsible for researching major means of improving manufacturing efficiency during World War II. The American automakers, comfortable with their own profits and confident in their future, didn't want to have anything to do with him, so Deming went to Japan and taught them how to make cars that were both more reliable and cheaper than the Americans'.
Plus, as a bonus, thanks to Article 9 of the Japanese Constitution prohibiting Japan from maintaining a military (though it never mentioned anything about a Self-Defense Force) and instead relying on the United States for military muscle via the Yoshida Doctrine and the current Security Treaty, the lucky ol' Japanese government doesn't have to worry about spending as much on defense as it normally would with China, Russia, and North Korea so close by and thus could pump a lot more money into public works, education, healthcare, infrastructure, and government subsidization of business.
A longer term issue for Japan which was overlooked by the people who believed Japan would take over the world is an aging and declining population. While other first-world nations also feature declining birth rates among their native populations, immigration is keeping populations levels slightly rising or steady which countries such as Canada, the United States, and Great Britain can handle relatively easily as they have a history of multiculturalism and multiethnic population. Japan, for assorted reasons, has essentially no immigration in comparison: in 2015 there were 9,469 applications for Japanese citizenship approved compared to a population of 127 million. Canada, with a population of about 35 million, averaged almost 11,000 immigrant citizens per month in 2013 (total of 129,000), the United Kingdom—with a population half that of Japan—had 118,000 new citizens in 2015, and the United States naturalized 653,416 new citizens in 2014. Japan's annual number of new citizens was therefore about 33% less than an average week in the United States.
This trend, which currently shows no sign of abating, means a greater and greater portion of the Japanese economy is going to have to be devoted for caring for an aging population with fewer younger people to carry that burden, which both reduces the amount of resources Japan could direct to other countries and the population to do it.