One of the possible consequences of an aggressive North Korea with nuclear capabilities is the remilitarization of Japan.
At some point, any and every nation that depends upon the US for its defense must assess
1) The threats it faces in terms of severity and imminence
2) The resolve of the US to defend it against these threats, and the limits to which the US will go even with the firmest of resolve
3) The degree to which the US will attempt to limit the nation's own response to the threat
The more imminent and severe the threat the less likely the nation and the US will completely align on limitations.
It is to be greatly hoped that North Korea will not attack Seoul with long range artillery or rockets, but let's say they do. Given that NK has nukes, and the US has interests and allies other than SK within NK's strike zone, how far would it go in retaliation, and how far will it allow SK to go?
According to GlobalFirepower.com Japan is ranked 9th in the world in military strength. By comparison, South Korea is ranked 12th and North Korea is ranked 20th. Nuclear capabilities are not considered in the rankings.
Despite the relative rankings, it would seem that South Korea is in a much better position to retaliate against NK than Japan if only because of geography.
Japan could likely manage retaliation to the sort of relatively minor provocative attacks referred to by Diest, but in the case of a more serious attack, it's probable that they would heavily depend on the US.
The likelihood that North Korea could deliver one of its nukes against Japan is very slim and against us, even slimmer. Of course Japan is a lot closer to NK than we are, and even if NK has the capabilities to shoot a nuke armed missile anywhere near US soil, we would probably pick it up on our defense systems and be able to intercept it. Still, there is a chance, albeit very small, that NK could nuke the US.
At the same time, we can't be sure how China will react in a situation where severe retaliation against NK might be called for.
In any event, the US is going to be very concerned about possible escalation and, in my opinion, more likely to downplay than overplay retaliation against any further NK attacks.
In the short term, Japan is pretty much stuck with its reliance on the US, but this is not a brand new turn of events and we can be certain that NK has been seen as a significant security threat by Japan for some time. If Japan has perceived or now perceives that the US has become less resolved or more limited in terms of defending Japanese security or, just as importantly, that North Korea believes this to be the case, it may decide that it needs to assume more of the capability and decision making in terms of its defense.
A remilitarized Japan has implications for a new arms race among Japan, China, North and South Korea and Taiwan.
I don't believe the world needs to fear a remilitarized Japan in terms of a return to military imperialism, but emotions about the Japanese still run hot in that part of the world and any build up of arms anywhere creates instability and increases the probability of a disaster.
At this point I will once again return to Iran because the current state of affairs on the Korean Peninsula underscores both the threat and the opportunity presented to us in the Middle East.
North Korea is a basket case. Its economy is in ruins, its culture is stagnant, its society has regressed to something quite dark and despairing, it has virtually no friends on the globe, and even if it has expansionist fever dreams there is no chance that they will be realized.
And yet look at how it is able to destabilize an entire region of the world, increase the probability of massive death and destruction, and foil and frustrate earth's greatest superpower... all because it possesses a few nukes.
Now think about this situation transported to a region of the world that is already the most explosive, is sitting upon, arguably, the engine of the global economy and is in closer geographical proximity to far more of America's interests and allies.
Then rest it in the hands of a regime that already considers us its greatest existential threat, has, for decades, been developing strong strategic alliances not only in its region but within our own, (as well as the rest of the world), and has very clear expansionist designs.
What mischief and mayhem will Iran make with only a few nukes?