There are two major issues that came about regarding the Japanese surrender. One arose on the Japanese side and the other arose on the American side.
On the American side of the debate was the issue of how firmly to demand unconditional surrender. The Allies had long stated that any Axis surrender would have to be unconditional. However, it was quite clear that this statement was making it harder for the Japanese to surrender. The Japanese believed that their emperor was part of an unbroken succession of emperors leading back into a mythical past in which the emperors were descended from the sun goddess. Therefore, they were very reluctant to surrender if the emperor might be removed or even put on trial. The US eventually started to strongly hint to Japan that the emperor would not be removed if Japan surrendered.
On the Japanese side of the debate was the issue of whether Japan should surrender at all. There was a strong feeling among many in the military that the country should not surrender. They felt that it would be dishonorable to surrender and that it would be preferable to fight to the death. Because of this, there were attempted coups when it became clear that surrender was being considered. There were attempts to prevent the emperor’s surrender speech from ever being broadcast.
Eventually, of course, these issues were resolved and Japan surrendered to the Allies.