We can reconstruct, I think, what the story must have been, from Coleridge’s brief précis of it. Perhaps it was something like this:
A painter was present at an exhibition of his works and overheard a spectator say, “This picture has too many black spots.” The painter was mortified and worked all night to correct the picture, but on the next day the same spectator returned and said, “This picture has too many white spots.”*
* albo lapidae notatae = marked by a white stone
That is, the spectator was motivated by a desire to criticize, not by any particular flaw in the work. This corresponds to Coleridge’s analysis of the motives behind the criticism of the Lake Poets, which he sees as deriving from
an unquiet state of mind, which seeks alleviation by quarrelling with the occasion of it
provoked by Wordsworth’s argumentative preface to Lyrical Ballads, and not by any particular detail of the poems:
the same general censure has been grounded by almost every different person on some different poem
As to the origin of the story, I have been unable to trace it. But it is similar in outline to an anecdote in Pliny about the painter Apelles of Kos:
Another habit of his was when he had finished his works to place them in a gallery in the view of passers by, and he himself stood out of sight behind the picture and listened to hear what faults were noticed, rating the public as a more observant critic than himself. And it is said that he was found fault with by a shoemaker because in drawing a subject’s sandals he had represented the loops in them as one too few, and the next day the same critic was so proud of the artist’s correcting the fault indicated by his previous objection that he found fault with the leg, but Apelles indignantly looked out from behind the picture and rebuked him, saying that a shoemaker in his criticism must not go beyond the sandal—a remark that has also passed into a proverb.
Pliny the Elder, Natural History, book XXXV, translated by David Edward Eichholz.
There is another mention of the story in Newman’s Tracts for the Times, though this postdates Biographia Literaria:
But once begin altering, and there will be no reason or justice in stopping, till the criticisms of all parties are satisfied. Thus, will not the Liturgy be in the evil case described in the well-known story, of the picture subjected by the artist to the observations of passers-by?
John Henry Newman, ‘Thoughts respectfully addressed to the clergy on alterations in the liturgy’, 9th September 1833.