The movie scenes the Clampetts watched were for a movie (Send Me No Flowers (1964)) which would be released in theaters the month after this was originally broadcast. This scene was effectively a coming attraction for the movie.
The entrance of Mammoth Studios is actually the entrance of General Service Studios, where the series was filmed.
Coincidentally, Mammoth Pictures is also the name of a fictional studio featured in Bud Abbott and Lou Costello in Hollywood (1945), as well as a few episodes of The Monkees (1966).
The episode opens with a sight gag of Jed whittling so much that Duke is completely covered in shavings.
With this episode, Curt Massey becomes the series' new composer.