The "German problem" was (and kinda still is) the fact that Germany is too big for Europe, but too small for the world, as Henry Kissinger put it. It's too weak to dominate the whole continent, but its neighbors will always feel threatened if/when it seeks alliances, because any alliance that includes Germany will destroy the balance of power.

Bismarcks "solution" was the creation of a whole system of alliances with pretty much every European player except France. Germany should fulfill its role in the middle of Europe by being in the center of many different alliances, having good relations to everybody else (again, except France) and by that creating a situation in which everybody depended on Germany. Berlin should be the spider in the middle, pulling its net just as it felt like. It should act as an "honest agent", mediating between every other power in Europe.

This worked very well for some time, but such a system can't survive forever. Sooner or later you'll get drawn into conflicts in which you should, in theory, be good friends with both parties (A.-H. and Russia, for example). Bismarck managed to keep this working by being a very skilled negotiator, but I feel strongly that there would've been a point where the increasing complexity of this solution had overwhelmed him too.

As it stands, Bismarck kept this system running. It's been called "juggling five balls at once" because the German chancellor, the most powerful man in Europe, had to keep the interests of (at least) the five Grand powers always in his mind and balance them out against each other. When he left, his successor Leo von Caprivi famously said that he couldn't juggle five balls at once. The best he could manage were two.

EDIT: Just found a nice picture of Bismarck juggling his five balls. Description only says, "American political cartoon 1887". http://files.homepagemodules.de/b83273/f14t5166p74226n2.jpg

And so this system collapsed.

After WWII, Adenauer and West-Germany decided that they didn't want to be the "honest agent" in the middle anymore. Adenauer said that it was completely impossible for a power like Germany to be independent in the middle of Europe because it would inevitably be drawn into every conflict thinkable but it would be too weak to actually solve or deter those conflicts. So it was no more independence in the middle, but strict integration in the NATO.

Today, the problem is back (kinda). The EU mitigates it so some degree, but still. The New Statesman had a great write-up on this, can be found here:

http://www.newstatesman.com/world-affairs/europe/2013/03/cracked-heart-old-world

I know that Henry Kissinger supports this view. You can read more about it in the early chapters of his book Diplomacy which is itself an interesting read despite the controversy that surrounds the man.

He outlines how Bismarck unified the German states and popularized a common German identity. He glorifies him as an excellent user of Realpolitik; a man who knew when to wage war and when to not. His successors (at least in terms of Germans who held as much swag as he did at his prime) were remarkably unsuccessful at implementing his level of diplomacy.

Kaiser Wilhelm's attempts to emulate Bismarck's policy and extend Germany's position within Europe led to German encirclement and a fear that it would destroy the balance of power system then in place. While Bismarck had alienated France from the rest of Europe, the Kaiser unintentionally created the allied bloc of nations that would defeat him in WW1 through the fear of German expansionism.

The reason that no one here is really touching on is that the bureaucratic and and diplomatic system of Germany was very complex even by standards of other nations. Part of the reason was that the German Empire has an enormously complex constitution, that most politicians and diplomats in the 1860s themselves did not understand. This is because there were many clauses in the constitution that were hidden so as to create a federalized state that also kept in tact the aristocratic power. The German Empire was trying to become a unified Empire. But the German Empire was in no way shape or form trying to move on as a democratic state.

The German Empire was already rather complex. The German Empire was a union of 25 states. These states all had their own separate governments, and not all were the same form of government. These were the Kingdoms of Prussia, Bavaria, Wurttemberg, and Saxony. The Grand Duchy of Baden. Free cities of Hamburg, Bremen, and Lubeck. Then the states of Oldenburg, Brunswick, Saxe-Meiningen, Saxe-Altenburg, Saxe-Weimar, Saxe-Coburg, Gotha, Anhalt, Schwarzburg-Rudolstadt, Schwarzburg-Sonderhausen, Waldeck, Reuss olderline, Reuss younger line, Schaumburg-lippe, kippe, hesse, mecklenburg-schwerin, mecklenburg-strelitz.

As you see there were some states that were just cities, some that were kingdoms in their own right, and some that were republic state. There was also Alsace Lorraine that was an imperial territory rules by a governor.

Furthermore the government had the Reichstag (parliament) that was elected by universal suffrage, the Bundesrat which was a federal council, the chancellor and the emperor.

The emperor himself had separate powers as the Emperor and as the King of Prussia for instance. The king of Prussia could appoint and dismiss any government official, including the Chancellor, they also could institute Martial law, summon and dismiss the Reichstag, and could declare federal execution against dissident member states and sequester their territory or rights of sovereignty, and could interpret the Constitution (like the supreme court of the USA).

The Reichstag and Bundesrat mainly had powers regarding economic and commercial issues. The Bundesrat could also change the constitution. But of 58 votes in the Bundesrat, Prussia controlled 17, essentially giving them a veto. The Reichstag also while being elected universally by men, wasn't really a democratic institution. The Reichstag could assent to laws, but it had very few powers when it came to initiating laws.

There were various things that show how complex the structure was though. For instance the federal government controlled matters of tarriffs, taxes, etc. which were collected locally but then sent to the federal government. But some territories (in southern Germany) like the Kingdoms of Bavaria and Wurttenburg were exempt from some taxes and could also raise their own troops, and were separate from the Prussian Army officers and chief of staff.

This all created a massively complex system. So while yes Bismark kept alliances with the majority of the European powers that wasn't the system that only he could master. He created a government that was extremely complex with various checks and balances amongst several bodies of government, with an emperor and kings within the empire, all of whom had separate powers. These all had to come together to get anything done, while keeping the power in the hands of the aristocracy. So while the German Empire was an unification of the German people, it was not like the United States in that is was of the people, it was a unification of states, that was dominated by the Kingdom of Prussia. To move laws and diplomacy forward Bismark had to move between the various systems of government, that he himself created.

source: Gordon A.Craig "Germany 1866-1945" pg 38-45