In the middle of watching Full Metal Jacket Here, posing this question: is it possible to buy a semi-auto Vietnam-era "mattel toy" M16A1?
Yes, kinda. If you really want to get as close as possible to the issued item you have to build it yourself for the most part.
Just a little extra background and a nit or two . The pic A4's posted is a Colt SP-1 which is a semi-auto version of a weapon that I think was only issued in limited numbers to some Air Force security units. I'm certain it was never issued to The Marine Corps and 99% certain never issued to any Army units.
As Junkball mentions the weapon issued to Marine and Army units at the time was the M16A1. Pictured below.
The primary difference between the two is that the M16A1 had a teardrop shaped forward assist and a partial fence on the lower protecting the mag release button. The SP-1 has neither. A few M16A1's with 3 prong flash suppressors were still being issued to grunts as late as 1978. Most of them I saw had bird cage flash suppressors similar to what you see today, and like the pic above. We liked having at least one weapon with a 3 prong suppressor around. They were great for twisting and breaking the 2 wires used to hold a case of C rats together. Pissed off the armorer though.
I loved the M16A1. It was much lighter than today's version and the sights were simple, rugged and effective once you got them sighted in. The M16A1 buttstock is slightly shorter than the A2 stock. (which I like enough to have retrofitted on my personal AR15s that don't have collapsible stocks)
Very early rifles had barrels with a 1-14 rifling twist rate but I believe all the ones we had were 1-12. The 55 grain bullets we used would barely stabilize at 1-12. It wasn't that uncommon to have rounds keyhole in a paper target at 500 yards. That said if you were any good they would keyhole in the black. That combination of a 55gr bullet and a 1-12 twist barrel was what gave the M16 it's well deserved rep for doing nasty shit to another human. For man killng out to 300 yards, an M16A1 loaded with 55gr rounds in a 1-12 barrel gives me a woody.
The challenges of building your own have mostly to do with finding the parts and the partially fenced lower. One with no fence like an SP-1 lower or ones with a full fence like modern lowers are not correct. Also the M16A1 and SP-1 are not black, they are "Colt gray", a color very difficult to duplicate. Once in a while you can find people making a run of M16A1 lowers and there are several good forums online with gouge on building old school M16A1s. It wouldn't suprise me to learn that someone was actually building complete weapons for sale but now a days I bet they would take forever to get.