The recent missile and nuclear tests carried out by North Korea present a major test for the efficacy and credibility of the United Nations and International Law in general. To understand why this is let us consider the situation as it now stands. For some time the international community has been working to have a peaceful resolution to the unfinished war on the Korean peninsula. But because of North Korea's push to develop nuclear weapons there is a perception that what the UN and the group of 5 nations (Japan, South Korea, China, Russia and the US) have been doing has not been working. There is still a lot of talk about renewing the negotiations and having a peaceful resolution to the crisis, but even if conflict is averted the UN and international law in general will have lost its credibility.
There are several possible outcomes to this crisis. Let us consider them:
The negotiations could either start back up, or not.
If they do they will either succeed or fail in disarming North Korea.
If the talks do not start up, then either action will be taken to disarm North Korea or no action will be taken.
Let us look at what these four possible outcomes would mean.
First, if North Korea is not disarmed either through negotiations or otherwise (the international community's inaction) then there will be perception that international law is of no effect and that any country can try to get nuclear weapons and no one will or even can stop them. This outcome should give cause for concern to countries like Russia who have to deal with countries like Georgia. If a small nation like Georgia sees that North Korea can get nuclear weapons and not suffer for it, they may look to build their own nuclear weapons. And if that is the case then what is there to stop countries like Iran, Venezuela, Egypt, Syria or Libya from building their own?
The whole purpose of the Nuclear Non-proliferation Treaty was to prevent more countries from arming themselves. If the treaty is shown to be ineffectual then many more nations will arm themselves, both for offense and defense. This does not seem to be a very pleasant prospect.
If Korea is disarmed (through negotiations or force) then there will be an understanding that international law and the UN do have power and they can enforce international treaties. The perceived strength of international law after this is accomplished will depend on the manner of the negotiations (or the force used).
Thus just as North Korea was the first major test of the UN, it may be the last major test of the UN. It passed the first time around, but if it fails this current test, there may be no further tests for the UN.
I should point out that there are possibilities that may allow for a peaceful resolution without such bleak or depressing outcomes, but a lot of that depends on some noble actions from people that up until now have not demonstrated much nobility.