That's part of why international legal proceedings are so difficult to justify. There is no broadly accepted set of standards by which to judge the actions of a sovereign nation, and most attempts to establish normative standards have failed -- not because some panel failed to come up with any, but because there's no practical way to insist that anyone conform to them. That's a problem that Arendt deals with in more depth elsewhere -- a more profitable examination of those problems is offered by E.H. Carr's "The Twenty Years' Crisis", and it seems to me that their points are largely consistent.
That leaves us with a couple of options -- by which I mean, historical precedents. One is to envision a higher court of authority, which, as I read it, is essentially what some post-war tribunals did by coining the notion of "crimes against humanity." We can set that aside at the moment, I think.
Another -- and this is the one that I think Arendt has in mind here -- is to try a sovereign state for breaking its own laws. Whatever degree that is effective depends largely on the state's unwillingness to contradict itself. That's largely because self-contradiction is a threat to one's claim of sovereignty.
I'm not sure I can really talk about why that's so without talking a little about how sovereignty works as a principle, so forgive me if what follows in this paragraph is old hat for you. Basically, states recognize one another's sovereignty because they want their own sovereignty recognized. And part of what motivates any given state to protect another is their desire to preserve the validity of the principle of sovereignty. If someone were to really set a precedent by making it politically possible to set aside sovereignty, the whole system of relationship between modern states would have to change. That's part of why a great many of the nations in the U.N. -- few of whom had any love for the Baath regime -- objected to the U.S. invasion of Iraq. Even if regime change in Iraq was good for most everyone, setting the precedent of ignoring sovereignty at one's convenience threatened a status quo that it was in everyone's interest to observe. So you protect the sovereignty of others (according to certain criteria) in order to preserve the principle that obligates others to observe your own sovereignty.
Certain forms of behavior can potentially invalidate a state's claim to sovereignty -- in other words, can free others from the obligation of recognizing sovereignty in that state's instance -- but they're not always determined by the considerations we'd like them to be determined by. Thus, having part of your industry reliant on slave labor may exclude you from membership to the U.N., but no one's likely to deny your sovereignty over that issue alone. Encroaching on another state's sovereignty is one invalidating act (as when Iraq invaded Kuwait and was in turn confronted by the U.S.); self-contradiction sometimes constitutes another.
If I understand Arendt properly, the acts-of-state argument serves as an exception to this. If a state violates its own legal principles, it may risk the censure of its sovereignty in the eyes of other nations. A consensus on the matter could be fatal. But if the state in question can convincingly argue that it's only being inconsistent (unjust) in order to preserve its ability to resume consistency (justice), then it may warrant a pass on the matter.
Which may be why you assumed Arendt had something similar in mind. It happens all the time. I'm sometimes re-read books and am shocked to realize how a change in my own context makes it obvious that the author was talking about something significantly different from what I initially supposed.
That's really easy to do with Arendt, so don't kick yourself over it. The sub-arguments that contribute to her total argument are often so involved that it's not at all difficult to lose sight of the wider context.
No prob. Talking it through helps me clarify my own thoughts on the essay, so it's worthwhile all around.