The Trouble with "The Enemy of my Enemy is my Friend", Historic Examples

Arthur Zimmerman, German Foreign Secretary in the 2nd half of World War I might serve as the "poster boy" for troubles with the principal that "The enemy of my enemy if my friend".  By inviting Mexico, via telegram, to "enter into an alliance with Germany against the United States in exchange for which she would regain 'her lost territory in Texas...'", he helped to finally bring the U.S. into the conflict.  He then played a major role in helping Lenin and a trainload of his followers reach an increasingly unstable Russia, where they did, just as he hoped, push Russia over the brink, practically eliminating the Axis' Eastern front.

Germany lost the war anyway, and Soviet Russia remained its biggest problem throughout most of the rest of the century.

But it took the Cold War to show just how much destruction could be wreaked by this principle.  In summary, by cultivating a motley assortment of backward nations as allies against the USSR, we either spread misery, or at least made the U.S. appear responsible for the misery of much of Latin America, the Near East, and Southeast Asia, and saddled countless poor nations with no experience of democracy with far greater powers of destruction than they could ever have developed for themselves.
[to be continues?]