I think some corrections need to be made here.
As far as I know, there were two revisions of the Apple III. The initial revision was released during May 1980, this was the one with all the problems. Apple attempted to fix the problems with a revised model released in late 1981, also called the Apple III. But then Regis McKenna, who did Apple's advertising back then, refused to promote the III anymore.
14,000 original systems were replaced by Apple with the late 1981 revised model. Even some of the replacements failed. Apple released the Apple III+ in December 1983. From what I can tell, the III had such a bad reputation that hardly anyone bought a III+, nobody trusted it!
Either way, all three revisions of this system are very rare, and you are very lucky to have one in your possession.
wood_e, when you open up the machine up, let us know if there's any indication of a Rev on the logicboard.
EDIT: If I'm talking rubbish, then feel free to correct me. It was back in 2006 that I researched the Apple III, and I haven't actually looked into the specific differences between the 1980 III, 1981 III, and the 1983 III+. It would be interesting to see if the III+ has a different layout inside, and I would imagine it also has a fan?