A couple thoughts:
His mention of his employment in the ad isn't really a reference, but it sounds like he's using his employment with the construction company as a qualification for the job. Since the ads were available to the general public -- and assuming that the employer was aware to some extent of Joe's ad -- you probably are not out of line contacting his boss -- and, while I don't know New York law, it sure doesn't sound like extortion or blackmail. On the other hand, I fear it won't get you much satisfaction, since my guess is the boss will want to have less than nothing to do with his employees' after hours gigs. If you talk to the boss, he is most likely to pull Joe aside and say something like "I got a call from a dissatisfied customer of yours. How you deal with it is your own business." That may or may not get any action out of Joe. Perhaps the mere threat of contacting the boss will. . .
The problem is what do you really want from Joe at this point? Since he displayed himself to be a thorough incompetent at panelling, do you really want him mucking around your den trying to make his bad work look better? Sounds ominous to me. Or do you want him to compensate you so that you can start over and get the job done right from the start without your having to take a major financial hit on the deal? That sounds ideal, but how likely it might be I have no idea -- maybe there's a mutually tolerable compromise that can be reached. By all means try to have a talk with him about it, but think about what you really want him to do for you . . . and what you're willing to live with.