There were many seemingly undesirable consequences of German and Italian unifications in Europe, but the biggest one of all was the Balance of Power.
The Congress of Vienna had established a balance of power between the Continent's biggest powers: Britain, France, Russia, Austria-Hungary and the Ottoman Empire.
German unification interfered with this balance. The germanic tribes that made up the symbolic "Holy Roman Empire" were a significant military power, but were weakened by squabbling amongst themselves. Uniting these tribes introduced a powerful military presence into Europe disrupting the balance established by the Congress of Vienna.
Italian unification also threw a wrench into the balanced structure, as well as being concurrent with several independence movements in the Balkans, weakening Austria-Hungary.
Ultimately European powers formed a new set of alliances and balances that one observer called "a powder keg."