According to the website Japan Today, film critics Ken Terawaki and Hiroo Otaka have been the most outspoken. Otaka wrote against the use of the scene in the movie magazine Kinema Junpo, noting that the scene narratively serves no real purpose and complaining that Indiana Jones (Harrison Ford) goes about his adventures unscathed. He also points out that children today -- in both Japan and the U.S. -- are unaware of the real damage caused by a nuclear blast. Other people have been expressing their disapproval on message boards, including one on the film's Japanese website. Not everyone is upset, however, and apparently some people are coming back with the "it's only a movie" retort.
Just to be accommodating, I think Steven Spielberg should include the short documentary Hiroshima Nagasaki August, 1945, which graphically shows the effects of at least an atomic bomb, as a supplement on the Japanese version of the DVD.