I bought a pair of IIIs in 1970, and I still have them. Mine came new with the whizzer cone on the midrange. When I blew one out, Rectilinear sent me a replacement that also had a whizzer cone, but a slightly different shape(!). Some time in the 1980s, the tweeters began to fail -- I suspect the wiring from the coils to the terminals on the baskets broke. This caused two or three tweeters (and/or supertweeters) to go quiet in my pair of speakers. The speakers are stored in my basement now.
I bought the speaker for its high frequency openness and dispersion. The speaker had two supertweeters and two tweeters, as well as the midrange and woofer loaded to a front facing ducted port. I seem to remember Julian Hirsch describing the effect of so many tweeters as almost electrostatic-like, back in a review in 1966(?). This was the speaker's strongest feature and really appealed to my taste at the time. Unfortunately, the use of four high frequency drivers located apparently randomly on the front baffle eliminated any chance for the coherence and imaging benefits of single tweeter systems. The bass was always pretty flabby, although the 12 inch cone and front ducted port could certainly move a lot of air. The midrange was cool, distant. With the whizzer cone, there was a slight cupped hands "aauu" coloration. There was really no "presence" emphasis like some of the JBLs of the time, and the whole midrange seemed a little shelved down.
I replaced the speakers in the mid-1990s with a pair of Thiel 3.6s. (I had lost interest in sound reproduction for a few decades and hadn't thought to upgrade my system until I read some kind of a retrospective in Stereo Review that compared the IIIs adversely with modern speakers.) The Thiels showed me what I was missing. In comparison, the Rectilinears were obviously deficient in coherence, imaging, high frequency extension, midrange freedom from coloration, tightness of bass, and extension of low frequencies beyond the upper/mid bass. (At this point, I became hugely bitten by the upgrade bug and gradually replaced everything in my system.)
For perspective, the Rectilinear IIIs were $279 (MSRP per speaker, mine cost $200 each) floor standers competing mainly against bookshelf speakers that were priced slightly lower (generally about $250 per speaker). The popular choices included the AR 3a, the KLH 5, the JBL L100, and, later and slightly cheaper, the Large Advent Speaker. With its floor standing design, emphasis on the middle of the treble range and formidable looking woofer, it offered an interesting alternative that became reasonably popular after a couple of favorable reviews in the audio press. After several years, Rectilinear offered another version of the III, with what seemed to be the same driver set packaged in an enclosure that looked shorter, wider, and accordingly more squarish from the front (versus the tall rectangular look of the original III). I never got the sense that these achieved the same popularity as the originals.
In sum, the IIIs are far from the current state of the art. However, they do have a distinctive sound character that may appeal to you, and this may be enough to offset its significant drawbacks. Have a listen.