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."