[LjubivojeRadosavljevic]

There are still conflicting reports on the exact time of death. Now there is a consensus that he was dead before the official time of death 8:30 AM, Dec. 17. However, one source says it was 8PM, Dec. 16 and the other claims that it was 1 AM, Dec. 17.

Why is this important?

[TigerLikesRooster]

It may shed the light on the situation in which he died. For example, is there any foul play involved? Was the regime having firm grip of situation or showing some chaos?
You can reinterpret activities of NK gov. officials and announcement in light of the timing, and you can get some insight into how the NK regime is working currently.

[InvisibleChurch]

One reason is that it shows the poor intelligence the West has on NKorea. Plus it is helpful to know when a dictator dies so contingency plans can be made to deal with a mad general or other batty official who might want to do harm to other nations.