In the original edition of RETURN TO BAG-END,* I noted in my discussion of Bilbo's riddling self-identifications of himself to Smaug that while most refer to v. specific events, there was an exception:
I am the clue-finder --this could refer to any of several episodes.
It might mean Bilbo finding the key to open the trolls' lair (page 97,
Chapter II) but more likely refers to his discovering the exact application
of the moon-runes on Thror's Map and thus enabling Thorin & Company
to find the keyhole at the exact moment on Durin's Day (Chapter XI).
Thanks to Anders Stenstrom, we can now narrow this down, and the passage should read as follows in the new edition:
I am the clue-finder -- this probably alludes to Bilbo's finding
the spider-thread and using it to guide his friends through the tangles
of Mirkwood in Chapter VIII, since 'clue' originally meant a ball of thread,
specifically the one used by Theseus to navigate the labyrinth
(Concise OED Vol I, page 434, under the spelling 'clew').
I am grateful to Anders Stenstrom for drawing this
etymology to my attention.
At the time I first drafted replacement text for this passage and posted it among the Errata on my website (Sacnoth's Scriptorium) [circa 2008, I think], I thought Anders' explanation was convincing, but more recently I came across some more information in quite another context that makes me certain of it. I was listening to an audiobook of an account of a famous murder from the early days of Scotland Yard, THE SUSPICIONS OF MR. WHICHER** by Kate Summerscale, which includes the following passage:
"The word 'clue' derives from 'clew', meaning a ball of thread or yarn.
It had come to mean 'that which points the way' because of the Greek myth
in which Theseus uses a ball of yarn, given to him by Ariadne, to find his way
out of the Minotaur's labyrinth. The writers of the mid-nineteenth century
still had this image in mind when they used the word. 'There is always a
pleasure in unravelling a mystery, in catching at the gossamer clue which
will guide to certainty', observed Elizabeth Gaskell in 1848. William Wills,
Dickens' deputy, paid tribute in 1850 to Whicher's brilliance by observing
that the detective found the way even when 'every clue seems cut off'. 'I
thought I had my hand on the clue', declared the narrator of The Woman
in White in an installment published in June 1860. 'How little I knew,
then, of the windings of the labyrinth which were still to mislead me!'
A plot was a knot, and a story ended in a 'denouement', an unknotting.
Of course, it this identification is correct (and I think it is), then Bilbo here is making reference to something that's no longer in the published story, since the whole 'Theseus theme' dropped out of the Mirkwood chapter and was replaced in the final book by the Enchanted River section. This it can now be identified as another fossil in the story, preserving evidence of an earlier version of the tale.
current reading: BLOOMSBURY PIE: THE MAKING OF THE BLOOMSBURY BOOM by Regina Marler 
**subtitle: A SHOCKING MURDER AND THE UNDOING OF A GREAT VICTORIAN DETECTIVE . It is Summerscale's thesis, which she demonstrates beyond any reasonable doubt, that this particular 1860 murder inspired the whole genre of the 'English Country House' murder mystery and exerted enormous influence on the detective story, esp. Wilkie Collins' THE MOONSTONE .