I remember those kits fairly well; I was working in a hobby shop when they were originally released. I only remember three of them, though: the Cutty Sark, Constitution, and United States. (To the best of my knowledge - and I'm more than willing to be corrected - no manufacturer has ever issued a kit labeled President. That's a little ironic, in that she's the only one of the three for which we have a contemporary set of plans establishing her War of 1812 configuration. The Monogram United States, is, if I remember correctly, bogus in that it doesn't have the raised "roundhouse" that the real ship did.)
There's lots of controversy about the various changes in her ornamentation over the years. Apparently her transom has, at various times, had eight, six, five, and three windows in it. (The famous "Isaac Hull model" in Salem, which is generally regarded as the best piece of evidence about her 1812 configuration, has six - with their muntons painted indigo blue.) I don't pretend to have any insights about when the transom configuration changed, but I have the impression that there were three windows in it during her last several active commissions - and her first several decades as a museum ship.
The Consitution's headrails were boarded up for many years, beginning in the mid-nineteenth century. (An 1858 photo I have in front of me shows her bow in that configuration - with the second of the two notorious Andrew Jackson figureheads attached.) During the 1920s she underwent a major restoration. (That was when the Navy started taking her seriously as a "museum ship." For some time prior to that time she'd had an incredibly awkward-looking roof built over her spar deck, dating from her days as a receiving ship.) The restoration was most definitely not carried out according to the standards of the conservation professions today - but it did save her for future generations.
In conjunction with that project the Navy published a set of plans, which showed how she looked when Lieutenant Lord (the officer in charge) and his contractors got through with her. Those plans were for many years regarded as "the official plans" of the ship. (It appears to have been in 1949, when Howard I. Chapelle published his History of the American Sailing Navy, that people started waking up to the fact that her appearance had changed a great deal since her construction.) Those post-restoration plans show the transom with three windows.
Most early wood Constitution kits (Marine Models, A.J. Fisher, Scientific, etc.) seem to have been based on those plans. So was the first Revell kit (the 1956 one, on 1/192 scale). Like the wood kits, it showed the ship as visitors to Boston saw her - with one big exception. For some reason the Revell designers included a nicely-rendered miniature version of the first Andrew Jackson figurehead.
I think (though I'm not sure; I haven't laid eyes on the kit itself for years) the little Monogram kit was also based on those Navy plans. If so, it more-or-less accurately represents her as she looked in the early twentieth century (though not when she was in active service).
We've discussed this kit a couple of times before here in the Forum. It certainly does have its limitations - many of them due to the fact that it was designed as a beginners' kit. At that time (the late seventies) American kit manufacturers were trying all sorts of desperate measures to attract new folks to the hobby; this was one of Monogram's answers to the problem. (It didn't work: it wasn't long after that the Mattel Corporation took over the direct management of Monogram, and the company stopped making serious scale models for several years.) It's a simple kit, but in many ways a remarkably ingenious one. Just how the designers managed to make a one-piece, hollow hull with at least a semblance of the real ship's tumble-home is something of a mystery.
Chapelle's books will only help a little regarding the Constitution's War of 1812 configuration. He did a tracing of the Admiralty draft of the President - which drawing is, as I mentioned, the only measured drawing that shows any of the American 44-gun frigates as they looked at that time. What Chapelle drew is, I think, reliable, but the drawing doesn't contain much detail - and only shows the hull and decks.
There are two good, comprehensive, non-contemporary sets of plans that do attempt to show how she looked in her glory days. One is the set drawn by George Campbell for the Smithsonian, when it was commissioning a model of her back in (I think) the early sixties. It's available via the Smithsonian. (We had a discussion recently of the rather elaborate procedure for ordering Smithsonian ship plans: /forums/1168958/ShowPost.aspx . The Campbell plans also were the basis for the Revell 1/96 kit.) The other option is the set prepared for the Bluejacket kit by a math professor named Lawrence Arnot in (I think) the 1980s. Arnot wasn't a professional draftsman (like Campbell), but he did a great deal of research; in terms of detail his drawings probably are at least as reliable as Campbell's. Unfortunately they're also pretty expensive: in the neighborhood of $60.00, I believe.