After going through a pile of label images that I’ve been collecting in the recent past, it seems like I can start to make some generalizations. They might be right. [Warning: a lot of these pictures have just been lifted from eBay auctions, most of them aren't mine.] [Warning 2: I may occasionally add more labels to this post as I see them.]
The oldest Apple ][ label I've seen (or at least have a picture of handy) is in this style, A2S1-4625:
That one enclosed a motherboard with date code 8040, which I have no reason to disbelieve based on the chip dates, which are all 1978-1980 that I could see. Which pretty much means that the motherboard was replaced along the way.
Here are a couple more. A2S1-8576, A2S1-16122 (7903, sadly the ][ lid was replaced by a ][+ lid during an upgrade), A2S1-16784 (8068?, replaced, appears to be a ][+ board, rev 4), A2S1-27105 (7919), A2S1-39587 (but motherboard was replaced with a ][+ board):
The next set of Apple ][ labels I've seen are the newer squarer ones, in red. Here the images I have jump to the 60000s, and perhaps there was a serial number "jump" somewhere here. But here are the red ones, A2S1-61786, A2S1-64313, A2S1-66077. I don't have board dates for any of those. And in any event, there's at least some cause for caution in trusting that the board that's in there is the one it shipped with. Note that A2S1-4625 had 8040 in it, while A2S1-27105 had 7919 in it. The 7919 board matches the timeline better, it's basically certain that the 8040 was a replacement. However, I've also seen 8022 and 8025 with all the hallmarks of an Apple ][ board (chip under slot 6, 16K select, flanged slots).
Moving on to Apple ][+, the serial numbers begin to start with A2S2, but the earliest ones are still in the earlier sticker style. The
oldest one I've got an image of (update: now "second oldest one I've got an image of," see A2S2-10087) is A2S2-11547, board date 7945 (along with what I originally took to be an "x", but which I now believe to be a "plus", signifying that this motherboard was built as an Apple ][+ rather than as an Apple ][, since it could have been either at the point of assembly). This board also has what I called above having "all of the hallmarks of an Apple ][ board", which leads me to suspect that it was an Apple ][+ fashioned from an Apple ][ (by adding the Autostart ROM chip), though on the other hand I think all of these characteristics can be present on the earliest of the (actual) ][+ motherboards.
Next comes A2S2-18606, same style. Board date hard to make out, but in the little bits I've blown up 4x, it appears to be 79xx. And same deal on this one, it looks like an Apple ][ board that was turned into a ][+ by adding the chip.
Then a big jump, new label style, lowest one I have encountered is A2S2-65001, board date 8006. But still the old hallmarks of an Apple ][ board.
I have various examples of this label style, all of these others seem to have newer revision boards where I can tell, with "N" pattern under slot 6, non-flanged slots, no 16K select chips, RFI attachment screws. A2S2-66915, A2S2-93277, A2S2-109180, A2S2-115091, A2S2-120955 (board replaced, had an RFI shield, and dated 8519, also oddly enough had a ][-non-plus lid), A2S2-122481, A2S2-149143 (8102), A2S2-161227 (8110), A2S2-164919, A2S2-174147, A2S2-179992, A2S2-359691, A2S2-362495 (0182), A2S2-403239.
The penultimate one there is interesting in that the motherboard inside it had a different date code style, listed as 0182, and stamped on rather than written on by hand (I don't have any evidence one way or another for the last one above). Somewhere between 161227 and 362495 this practice must have changed. All dates I've seen before this are in YRWK order (or at least YRxx for some xx, there is a single example I've seen (shown above among the Apple ][ labels, where the board has a date code that appears to be 8068, which is clearly not YRWK unless it is a sloppily written 8008, which it could possibly be). Perhaps it was simply just the practice in 1982 and beyond, since I have a couple of (poor) examples above of 81xx dates as well.
At this point, the labels switched style again, to the newer, busier one, with a dot matrix serial number. A2S2-448225, A2S2-472596 (3782), A2S2-512896, A2S2-544771, A2S2-546018 (4782), and the highest two serial numbers I have actually seen, A2S2-569185 and A2S2-588496 (on empty cases).
Here are my own newer two Apple ][+es as well, for comparison, A2S2-412783 (1782), and A2S2-542439 (4682).
One thing I observed here is that somewhere between 512896 and 542439, the model number changed (from A2S1048 to A2S1048A). There is no reason to think that this disrupted the serial number ordering, however, just as there is no reason to think that there was any serial number reset along the whole A2S2 line. In fact, looking back I think it might even be true that the serial numbers weren't reset even between A2S1 and A2S2—both A2S1s somewhere before 61786 and A2S2s somewhere before 65001 had the older style labels, then both switched. So, since we know any what that Apple ][ and Apple ][+ co-existed for a while, I expect that the serial numbers were still unique per machine, regardless of model.
Wikipedia reports that the Apple ][ was introduced in June, 1977 and discontinued at the beginning of 1981, an estimated 40,000 having been sold. It also reports that the Apple ][+ was introduced in June, 1979, and apple2history.org reports that it was discontinued in December 1982. I can't seem to find a source for the number of Apple ][+es sold. However, the estimate of A2S1s sold is quite a bit lower than the 66077 represented in the latest serial number I've found, suggesting that A2S2s were eating up some of the serial numbers.
Next up are the Bell & Howells. They took on A2S3 as a designation. These, unlike the A2S1s and A2S2s, seem to have their own serial number stream, and had model numbers like A2S10xxB. The earliest one I've found is A2S3-001522 (no backpack). The rest are A2S3-008426 (no backpack), A2S3-011082 (backpack), A2S3-016147 (no backpack), A2S3-021075 (no backpack), A2S3-022390 (5281, no backpack), A2S3-023165 (no backpack), A2S3-031522 (backpack), A2S3-033219 (backpack). The last two are also extremely high serial numbers for a Bell & Howell, usually the estimates are of about 20,000 sold, but it looks like maybe it was over 30,000. Also interesting, perhaps, is that the Bell & Howell label for the late-style label is slightly different, redesigned to fit the late-style Apple label underneath.
That last three are kind of interesting in that they use the last style of Apple ][+ labels. Also, it appears to me that the ones the came with the backpack (sample size above: 3) had the Bell & Howell black and silver sticker stuck overtop the Apple sticker. Perhaps this makes sense, since the backpack is what allowed the thing to be UL listed and suitable for use in schools? Anyway, the sample size increases to 4 for this generalization when I add in my own (below), A2S3-011472 (backpack). I think by now I'm relatively confident of the correlation.
Actually, having written this much, I remembered this post from 2007, which did a similar kind of forensics. For A2S1, he has never seen a black on white sticker above 40000, or a red on white sticker below 60000. My labels conform to this, perhaps there was an actual jump to 60000. I have also not seen a green on white (bigger, simpler) sticker on an A2S2 below 65001. Perhaps 60000 to 64999(?) were printed as A2S1 and 65000(?) on were printed as A2S2? It could be, although that means that that 65001 is a pretty special machine. I've beaten his record high on A2S2 (which was 544703), though: I've got a picture of 546018 (4782). I have a picture of two that are even higher, 569185 and 588496, both of which were on an empty cases. Which I'm now suspecting were never used in building a machine, production having shut down first. My terrarium motherboard is rev 4, I'm pretty sure, which doesn't match his specs (my terrarium board is 8050, he'd capped rev 4 at 8030).
All of this brings me back to my oldest ][+, the terrarium, however. Which is the real reason I got into this: What in the world is going on with this label? A2S2-1497165 (8050)?
That sounds crazy. The sticker style and board date and the old-style board should have put this somewhere around 65000-149000. We know 65001 (8006) printed ok, and the next serial-board pairing I have is 149143 (8102), which is in the neighborhood of 1750 machines/week assuming no variation, so perhaps it should be around 142000 (as long as it is assumed that 66915, 93277, and 115091 had their motherboards replaced, since those were all RFI boards). So was this supposed to be A2S2-147165 and an extra "9" got in there?
Later note: The serial number on the box of the Apple ][+ listed at vintage-computer.com (1492548) is a similarly crazy one, so my machine might not be the only one. No picture of the actual label or the motherboard to allow me to compare it, though.
I don’t think there’s going to be any way to tell, without hearing a story from someone who saw this glitch happen, if that’s what it was.