According to Urban Dictionary and The BS Dictionary: Uncovering the Origins and True Meanings of Business Speak (here): "The leading theory for where put a pin in it comes from is World War II, when soldiers were encouraged to put a pin back into an active hand grenade so it wouldn't go off. However, we have no credible sources to back that up."
What I love about this gloss is that the "BS" in the title (The BS Dictionary) is intended to suggest both "B[usiness] S[peak] Dictionary" and "B[ull] S[hit] Dictionary"—implying that "Business Speak" is Bull Shit (hilarious)—and that Bob and Tim's dictionary uncovers "the Origins and True Meanings" of said Business Speak / Bull Shit. In reality, the gloss itself is BS: "The leading theory for where put a pin in it comes from" is not from hand grenades and World War II, this is simply the first answer Bob and Tim discovered in precisely 1.4 seconds of Googling time (which led them to Urban Dictionary). So, rather than being a glossary to Business BS, The BS Dictionary is a Business glossary comprised of BS (also hilarious).
As for "put[ting] a pin in" something, most of the explanations offered for the origin of this term are based on thumb-tacks / drawing pins, which "conjures an image of somebody attaching a flyer or a notice to a cork board," "pin[ning] fabric in position before sewing it" in place or setting up pins in a pattern to create "bobbin lace" and stopping stitches you have finished from coming undone. Other suggestions relate to "pinning together pages of a book" or using "pins to mark edits in [a] manuscript"—something Jane Austen is credited with doing, apparently.
My own suggestion is rather more directly related to the meaning of the phrase, which is to "note carefully" or "bear in mind" (as glossed by Jonathon Green's excellent Dictionary of Slang, here): using a sewing pin as a bookmark.
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As you can see in the photos above and below, sewing pins were used as bookmarks in the eighteenth century. In this copy of Ab.16.8a2 La Belle Assemblée, 4th ed. (Dublin, 1740), vol.1, a pin has been inserted between two pages in such a way as not to fall out when the book is opened. That is, the tip of the pin has been pushed into the fold between pages 142 and 143, then downwards parralel with the spine, so that it becomes lodged in the paper, glue and binding, with only a short section of the shaft visible when the book is opened.
By inserting the pin in this way, the reader has marked the opening much more securely than is possible with the sort of loose bookmarks I typically use: a piece of paper or cardboard, that tends to fall out when the book is not kept firmly closed.
I noticed quite a few of these sewing-pin bookmarks, inserted in the same way, when I was physically examining hundreds of eighteenth-century copies of works by Haywood, for my 2004 Bibliography. Unfortunately, I did not make a note of which specific copies contained these pin-bookmarks, but I did examine the pins closely enough to be sure that they were definitely contemporary, hand-made silvered brass or steel sewing pins.
How did I know this? Well, at first I didn't, but seventeenth and eighteenth century pins have a very distinct look since, as is explained here: the pin itself [is] made of brass wire, [and] the heads were made separately of brass wound around the top of the pin." Pin-making machines were invented in the early nineteenth century (as Wikipedia notes [in a rather pathetic entry on pins]). These eighteenth-century pins look quite different from any pin I'd handled before, so I started looking into it.
Since my interest in any eighteenth-century reader records has only increased over the years—any evidence of reading really—it was with great satisfaction that I discovered that a contemporary reader of my copy of La Belle Assemblée had "put a pin in it"—"note carefully" so as to "bear in mind" the text.
Of course, despite it's very sharp point, a pin does not have much precision when marking text in the way we see here; less than a modern printed cardboard bookmark, since printed bookmarks typically have a front and a back, a top and a bottom, allowing you to indicate the top or bottom or a specific page. A pin is also more cumbersome than a pencil or ink pen for marking a passage. Moreover, if you were to attempt to mark a line, paragraph or single page, by threading it into and out of a leaf parallel to the outer margin of the relevant text, the pin would inadvertently mark text on both sides of the leaf, since the pin would be visible on both sides of the leaf—though the side of the leaf with the pin head might be the equivalent of the front of a bookmark.
On the positive side, although a pin-threaded-page may be difficult to find again, requiring the reader to fan through the whole book until the page with the pin it was found, it would be easier to find a pinned page than a page with a line of ink or a pencil mark on it. But if you were to attempt to mark—as some readers do—dozens of passages, you would have difficulty closing a book stuffed with so many pins, and it would be an expensive way of marking the text. Since pins were handmade, they were more expensive that the machine-made pins that followed.
So, why use a pin rather than a pencil or ink pen, if it is more cumbersome, costly and less exact? My guess is that a pin was simply close at hand—very close. I suspect that our pin-wielding memorialist used a pin because she was (singularly or, more likely, in company) engaged in multi-tasking: either alternatively or (to the extent possible) simultaneously engaged in both reading and sewing. Also, one of the first recipes that Eliza Haywood included in her Present for a Servant-Maid (1743) was "How to get Spots of Ink out of Linen" (here)—a reminder that ink and linen were a bad combination, and that handling ink and any material while sewing was a bad idea. It was far easier and safer to use a pin than to risk having to soak the linen "all Night in Vinegar and Salt, the next Day rub the Spots well with it, as if you were washing in Water, then put fresh Vinegar and Salt, and let it lie another Night, and the next Day rub it again."
As well as being easier and safer to use a pin, rather than ink, it is also cheaper and less damaging to the book, since the pin can be re-used / moved and—when used as here—leaves only a tiny and discreet hole. The fact that the pin remains in place in my copy of La Belle Assemblée could be interpreted to mean that it was deployed as a long-term marker, like ink or pencil, but it seems much more likely that it was only ever intended to be a temporary place-holder and that this pin remains in place simply because it was forgotten.
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In terms of moral alignment, using a pin as a bookmark might identify the reader a being somewhere between "true neutral" and "chaotic neutral" (alignments which cover bookmarking behaviour ranging from using a visiting card or bus ticket, through to using weird 3D objects to mark your place: pen, glasses, seed pods and [unused] condoms**) rather than lawful, neutral or chaotic evil (a continuum of place-holding and memorialising from dog-earing pages, highlighting passages, to tearing out pages you like and glueing them to the wall††). Generally-speaking, this sort of chaotic evil bookmarking is frowned upon, but from the perspective of someone writing a book on eighteenth century readers, it is actually quite welcome.
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To return to our phrase, it may be that "putting a pin in it" was once quite common, though evidence may be lacking for a variety of plausible reasons: the preference for pristine (unread) copies in the book trade and among librarians dooming genuinely "used" books; an historical librarianish disapproval and neat-freakery, which erased the evidence of reading from the few examples that made their way into institutional collections, i.e., due to librarians removing any pins present so that they can't rust or otherwise mark the pages; or the pins may have been removed by collectors interested in the curly-headed pins themselves. I have certainly collected a few historical pins for this reason, if not in this way.
Whatever the reason for pinned pasages being uncommon today, it would certainly be consistent with the period in which the phrase arose (early 18C; earlier than recorded in Green's Dictionary, to judge from the quotes provided on Stack Exchange) and with the meaning of the phrase (to "note carefully" or "bear in mind"), for "to put a pin in it" to pin a passage as we see here. Also in favour of my interpretation is that my book may be considered primary evidence: where is the equvalent evidence for the alternative interpretations?!
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**One of the few eighteenth-century condoms known to survive—one held by the British Museum—was found in a book in the Brish Library's Private Case, marking a passage where condoms were being discussed. An image of this condom appears in the exhibition catalogue London 1753 (2003), 144, No.3.20.
††Mary and Charles Lamb decorated the walls of their (rented) garret in Temple Lane, by cutting engraved illustrations out of their books and gluing them to the walls. Mary described the process in a letter of 2 November 1814:
"My brother and I almost covered the walls in prints, for which purpose he cut out every print from every book in his old library, coming in every now and then to ask my leave to strip a fresh poor author … There was such pasting, such consultation upon these portraits, and where the series of pictures from Ovid, Milton and Shakespeare would show to most advantage, and in what obscure corners authors of humble rank should be allowed to tell their stories … To conclude this long story about nothing, the poor despised garret is now called the print room, and is become our most familiar sitting-room" (here).