The Ballad of Jed Clampett has been replaced on the public domain sourced episodes of The Beverly Hillbillies due to copyright issues. Reportedly it has been restored for the official DVD releases by CBS but season four does contain other music changes.
As of this post, CBS has released the first five seasons of Beverly Hillbillies on DVD. Seasons 1-3 and 5 are, as far as I can tell and have read, uncut. The first three contain most (not all) of the original sponsor spots too.
Only Season 4 has confirmed edits. One scene (in Hoe Down a-Go-Go) is cut short to edit around a band (The Enemys) singing their cover of Pretty Woman on-screen. The edits include a few seconds removed, and a zoom-in that makes one visual joke difficult to see. This way they could replace the song without leaving evidence that the band’s lip movements didn’t match. Other than that, there were two other episodes (Jethro Gets Engaged and Jethro Goes to College) that had incidental music replaced (just one clip per episode). The new incidental music does not seem natural to the era/style, so it is noticeable too. I suspect that CBS just couldn’t confirm ownership of these particular pieces.
In summary, four of five seasons are uncut, and even the one that is edited only has minor edits on three episodes. The theme song is always present, as are Flatt & Scruggs’s many appearances. Releases with the theme song replaced are always unlicensed public domain releases. I highly recommend all five seasons currently available and hope that CBS releases the remaining four. These are the only way that we are getting original-length cuts of episodes not previously released on VHS.
Because this is a restoration forum, I’ll note that footage from the syndicated airings (available on YouTube) can be used to fix two (Hoe Down a-Go-Go and Jethro Goes to College) of the three edited episodes (including the one with the more extensive video edits). The other one (Jethro Gets Engaged) has the incidental music over a lengthy establishing shot (Jethro driving to the movie studio) that is edited out in syndication, so it cannot be restored using known recordings.