Has human-generated entropy ever been a real problem? I know the topic of human brains generating random numbers has been discussed here and in Cognitive Sciences before, but I am interested in a particular part of it:

In an introductory book to cryptography I read recently ("Cuando la criptografia falla", by Arturo Quirantes), it is mentioned that in some historical occasions, mecanographers were used to generate random numbers for cryptographic purposes. However, as we know now, it was not truly random (or at least uniformly distributed) and some numbers would appear more than others. I had read about this before, but I have failed to find examples of historical events when this technique was used. I am also curious about whether any important information has ever been leaked because of the low entropy of human-brain generated numbers.

Could you please point me to some documentation about this?
In World War II, this practice of generating "random" code books by hand is known to have been used by the Special Operations Executive, or SOE:


  Various techniques have been used to do the random generation. Marks
  describes how SOE agents’ silken keys were manufactured in Oxford by
  little old ladies shuffling counters.


(Security Engineering: A Guide to building Dependable Distributed Systems)

The Marks mentioned there is Leo Marks, who was the cryptographer for SOE.  His book Between Silk and Cyanide describes a meeting with Commander Denniston of Bletchley Park:


  [Commander Denniston] questioned me closely about WOK-production, and
  wanted to know why we preferred keys made by hand to the machine-made
  keys supplied by Bletchley.
  
  I explained that Bletchley hadn't produced them in sufficient
  quantities, and that the ones which they'd sent us didn't seem to me
  as random as the keys the girls produced by shuffling counters.
  
  He looked at me doubtfully, so I gave him six sheets of keys produced
  by the girls, and six by Bletchley.  He correctly identified
  Bletchley's, agreed there was a pattern to them, ...


(WOK stands for Worked Out Keys, and is a hand-enciphered code using shared random keys to seed it)

While I'm unable to cite a specific instance of hand-generated random data being insufficient, I'm sure it happened.  The coding systems used in World War II, both manual and machine-based, generally relied upon unpredictable keys rather than strong cryptographic algorithms.  Attacks upon keying material were the primary focus (again, both by hand and by machine).  Any weakness in randomness could be exploited.

When you consider the fact that the systematic and massive compromise of Enigma was kept largely secret for around 30 years, the likelihood of a particular hand-shuffled one-time pad being compromised and documented as such is pretty low.  So the fact that examples don't abound isn't really noteworthy.

Neal Stephenson's fiction novel Cryptonomicon does include such a story (although, again, it's fiction) - Detachment 2702's one-time pad traffic is decoded for a few reasons, including re-use of pads but also insufficient randomness:


  "Enoch, why are you . . . here?"
  
  "Oh. I am here, in a larger sense, because Mrs. Tenney, the vicar’s
  wife, has become sloppy, and forgotten to close her eyes when she
  takes the balls out of the bingo machine."