Yoshio Hachiro's stint as the Minister of Economy, Trade and Industry in the new Yoshihiko Noda administration was not the briefest cabinet assignment on record, but it was certainly one of the most controversial. News outlets reported that it was "public outrage" over two remarks he made which forced Hachiro to quit. In the absence of evidence, we have to take their word for it.
One of the remarks, that the area around the crippled Fukushima nuclear reactor was a "town of death," supposedly offended the people who had been evacuated from the region, but the media have been describing the place in similar terms for months now. The Japanese Twittersphere is still buzzing that it wasn't the public that was offended by Hachiro's remark but rather Tokyo Electric Power Company, which is still working out a payment system for residents harmed by the accident. Hachiro stated at his news conference when he assumed the METI position that "in principle" he would work to phase out nuclear energy.
Hachiro's other transgression, a joke about contaminating reporters with radiation after returning from Fukushima, is more problematic. It's obvious that at the time he allegedly made the joke Hachiro thought what he said was off-the-record, but as journalist Masaru Sato commented on Fuji TV, the ground rules for what's on- and what's off-record in Japan are "vague," and since every media outlet printed or broadcasted a different quote it's not clear exactly what Hachiro said or who first decided to report it. During his resignation news conference he apologized without actually owning up to the joke. One unidentified reporter interrupted Hachiro in a derisive tone and was shouted down by another journalist. A Kyodo News editor pointed out on TBS that news conferences are for asking questions, not for "prosecuting public figures." The joke, if he made it, was certainly careless, but given Hachiro's gregarious personality it likely sprang from a misplaced sense of camaraderie rather than from any cynical impulse. What he didn't understand is that the press, no matter how friendly they might seem, is waiting for such a moment since gaffes are so fun to report.