The phrases to be all fingers and thumbs and to be all thumbs mean to be extremely clumsy (i.e., lacking in manual dexterity).
Both those phrases are among the numerous variants of the original phrase each, or every, finger is a thumb, which is first recorded in A dialogue conteinyng the nomber in effect of all the prouerbes in the englishe tongue compacte in a matter concernyng two maner of mariages, made and set foorth by Iohn̄ Heywood (London: Thomas Berthelet, 1546), by the English playwright and epigrammatist John Heywood (circa 1496-circa 1578):
He maketh hauok. and setteth cocke on the hoope.
He is so laueis, the stocke begynneth to droope.
And as for gayne is deade, and laied in tumbe.
Whan he should get ought, eche fynger is a thumbe.
Eche of his ioyntes agaynst other iustles,
As handsomly as a beare picketh muscles.
The English naturalist and theologian John Ray (1627-1705), too, recorded the phrase each, or every, finger is a thumb in A Collection of English Proverbs Digested into a convenient Method for the speedy finding any one upon occasion; with Short Annotations. Whereunto are added Local Proverbs with their Explications, Old Proverbial Rhythmes, Less known or Exotick Proverbial Sentences, and Scottish Proverbs (Cambridge: Printed by John Hayes, Printer to the University, for W. Morden, 1670):
When he should work, every finger is a thumb.
Among the numerous variants of that original phrase, the following two are:
1-: From the transcript of a court case, published in The New-York Evening Post (New York City, New York, USA) of Saturday 17th April 1819:
“Like people that wear mittens. No wonder they are awkward, and all their fingers like thumbs, as the saying goes?”
2-: From Autobiography of an Amateur Singer. No. I., published in The Harmonicon (London, England) of May 1831:
The majority of humankind is born with eight fingers and two thumbs, and, unless in the case of those whose fingers, as the Irishman said, are all thumbs, practice and assiduity will eventually accomplish a violinist, oboeist, or any other ‘ist’ belonging to an orchestra.
The earliest occurrences of the phrase to be all fingers and thumbs that I have found are as follows, in chronological order:
1-: From The Islets of the Gulf; or, Rose Budd, by the U.S. novelist James Fenimore Cooper (1789-1851)—as originally published in Graham’s American Monthly Magazine of Literature and Art (Philadelphia, Pennsylvania, USA) of May 1847:
She had often heard the saying that “three half-hitches lost the king’s long-boat,” and she busied herself, at once, in repairing so imminent an evil. It was far easier for the good woman to talk than to act; she became what is called “all fingers and thumbs,” and in loosening the third half-hitch, she cast off the two others.
2 & 3-: Agricultural applications of the phrase to be all fingers and thumbs to vegetables:
2-: From the reply to a correspondent, published in The Cottage Gardener: A Practical Guide in Every Department of Horticulture and Rural and Domestic Economy (London, England) of Thursday 6th November 1851:
Carrots growing forked (H. E. M. O.).—We think that sowing these in ground with a rich surface is the cause of their being forked, or, as you describe them, “all fingers and thumbs.” If sown in trenched ground, with a little manure turned in with the bottom spit only, and with the soil not rich, we think you will have straight Carrots.
3-: From the review of The Journal of Agriculture and the Transactions of the Highland and Agricultural Society of Scotland, published in the Dundee, Perth and Cupar Advertiser (Dundee, Angus, Scotland) of Friday 16th July 1858:
The Journal of Agriculture, circulating as it does among the ruddy-faced, stout-limbed farmers of Scotland, shows that the agricultural mind which appreciates its excellent articles is as vigorous and healthy as is the physical condition of the farmers themselves. The paper on turnips proves that it is possible to wax eloquent even over this bulbous esculent. We are shown how bones turn to turnips, and how turnips again are turned to bones. We are instructed in the difference between the turnips civilized and uncivilized, and are duly impressed with the fact that the globular root, now so proper a member of the vegetable world, was once an erratic barbarian, all fingers and thumbs, and that education, training, and good management, elsewhere so useful in forming the gentleman, have not been thrown away when bestowed upon a—turnip.
4-: From the account of a meeting held at Kirkcaldy by Preston Bruce, Member of Parliament for Fifeshire, published in The Fifeshire Advertiser (Kirkcaldy, Fife, Scotland) of Saturday 3rd December 1881:
Questions having been invited—
An elector rose in the body of the hall, and made some vehement but utterly unintelligible remarks, which caused some noise.
Mr Hogarth, West Mills, stood up to ask a question, but
The elector rose again proceeded to speak, remarking that Mr Bruces [sic] performance was “all fingers and thumbs.” (Laughter, and “Put him out.”)
5-: From The Evening News (London, England) of Saturday 14th April 1883:
MORE OR LESS COMIC CLIPPINGS.
(From Funny Folks.)
An ecclesiastical contemporary has inserted a letter from “A Despairing Protestant,” who writes that “a Ritualistic vicar preached on Palm Sunday with ‘palms’ in his hands.” We really see nothing remarkable in that, since it would have been a case of “all fingers and thumbs” had his hands been without palms.
6-: From Effie and her strange acquaintances; a very curious story, almost true (Chester: Phillipson and Golder – London: Griffith, Farran and Co. – ), by the Rev. John Crofts:
She listened, and then she heard, distinctly, a small, but clear and ringing voice, with a tone of warning in it, singing the following words:—
“Ye Cowslips, give ear;
An enemy ’s near!
Ye Blue-bells, ring out an alarm!
A gawky thing comes,
All fingers and thumbs,
With a sandwich under her arm!
“That is a very odd song,” said Effie to herself; “I wonder what it can mean?”
7-: From the account of a rugby match between Durham and Lancashire, published in The Northern Echo (Darlington, Durham, England) of Monday 27th January 1890:
The passing tactics of the home team which now ensued were lamentably poor. Not one could stick to the leather when passed. They seemed all fingers and thumbs, and the ball would glance off and away the moment they touched it.
The earliest occurrence of the phrase to be all thumbs that I have found is from What is Compulsory Education?, published in The Echo (London, England) of Wednesday 16th November 1870:
Of all, ratepayers or not, we would ask,—Do they wish the productive forces of the country to be indefinitely augmented?—a million fingers more nimble, a million brains more cunning? Unless endowed with exceptional gifts, allowing for want of book learning, your uneducated man is all thumbs, as the phrase runs; and what education does for him is to supply him with clever fingers.