... is when manufacturers of some DVDs and video tapes replace the original
theme music with different music. These are usually "bargain bin" tapes and
DVDs of such shows as THE ANDY GRIFFITH SHOW, THE BEVERLY HILLBILLIES,
and BONANZA. Can someone explain how TV episodes can be in "the public
domain" while the themes from those same shows are not? One manufacturer,
GoodTimes, prints a disclaimer (in very small print) on their packages that reads: "These programs do not contain the original ... theme music. This video is not authorized by [the producer] or any other entity." Can anyone explain this
apparent anomaly?

I have noticed that to. I think it has something to do with the music copyright or something. I can't stand it either though. I

GF is on the right track. I can only speak to the The Andy Griffith Show episodes, but it probably applies to the other series as well. By accident, sixteen eps from season three did not get their copyrights renewed so fell into public domain. The theme music is under separate copyright that is still in force. This means that anyone can reproduce and sell copies of those eps without paying any royalties, but if the original theme music is used royalties for that must be paid. Most companies that produce those tapes/DVDs use other, probably free, music for the theme rather than pay for the original.

GF is on the right track. I can only speak to the The Andy Griffith Show episodes, but it probably applies to the other series as well. By accident, sixteen eps from season three did not get their copyrights renewed so fell into public domain. The theme music is under separate copyright that is still in force. This means that anyone can reproduce and sell copies of those eps without paying any royalties, but if the original theme music is used royalties for that must be paid. Most companies that produce those tapes/DVDs use other, probably free, music for the theme rather than pay for the original.
Thanks for clearing that up.