I think the answer to this question would depend greatly on your definitions of "near," "faultless," "libertarian," "socialist," and "anarchist."

The most glaring fault in the Republican territories was the rampant anticlerical violence. In total, 6,832 clergy were killed. (Jose M. Sanchez, The Spanish Civil War as a Religious Tragedy) In addition, the lawlessness that occurred in the wake of the coup was far from perfect. Given the ideology that the state had created the criminals or the conditions that made them criminals, many terrible people were released from prison. Some of these people returned to a life of crime and used the confusion to return to their previous activities--thievery, murder, and even rape. (This is best detailed in Paul Preston's The Spanish Holocaust, where one can find many examples of these incidents)

On the economic front, forced collectivization wouldn't fit the libertarian ideal, but it does fit some socialist ideals. Some of these measures had excellent results. Others, especially in agriculture, were less successful. Not only was there a good bit of resistance from large landholders, the smaller landholders weren't keen on giving up all they had worked for. Some of the collectivized farms were abandoned or neglected, and some harvests were left to rot. Given the shortages in the Republican zone, any such losses were keenly felt.

Further, there were small fiefdoms set up by some anarchist bands. I guess this could be viewed as an ideal method of voluntary local government, but it was certainly inefficient at times during the war. Some of these groups were purely ideological. Others extorted their ostensible allies over anything that moved through what they considered to be their territory in order either to enrich themselves or to fund the activities of their own military units.

From my study of the Spanish Civil War, there was hardly anything perfect about it. If you want to study the conflict in broad terms, there are three major books: Hugh Thomas: The Spanish Civil War, Paul Preston: The Spanish Civil War, and Antony Beevor: The Battle for Spain. For the violence during the war, there is Paul Preston's The Spanish Holocaust and Jose M. Sanchez's The Spanish Civil War as a Religious Tragedy. There are also a number of books on the revolution itself, which is an area I am less intimately familiar with. While some still romanticize one or another faction in the Spanish Civil War, the more sober historians have lost most of their romanticism over the years.

Also, I am unsure if anarchists, libertarians, and socialists would agree on a single definition of how a faultless society would be described.