Legally speaking, would a treaty signed in, say 1890, still apply to the German government of today if it had never been rejected? Does this go for the Weimar Republic (since it was the direct successor) too?
Generally speaking, when can you speak of a new state and when of a continuation of an old state?
In the case of Germany the Bundesverfassungsgericht (court for matters of the constitution) decided in 1973 that the German Empire endured after 1945 and that the Federal Republic is in fact identical to the Reich albeit only partially in the geography; the founding of the FDR was deemed a reorganization (http://www.servat.unibe.ch/dfr/bv036001.html#Rn079).
Generally it's an extremely complex topic as International Law isn't given by some kind of legislative body and isn't executed by some kind of executive body (even though the UN tries it's best to change some of these parts). There is no clear cut definition of state which works generally for all constellations (think about the Republic of China, Northern Cyprus, Kosovo, the Koreas, FDR and GDR, ISIS, …) so the definition of a successor state is even more complicated. Both Taiwan and China would probably call itself successor to the Republic of China but is e.g. the current Croatia a successor of Austria-Hungary or the Francia of Charlemagne or the Roman Empire? In international law it often comes down to the questions “What do the other countries think about this?” and “What are they going to do about it?”.