I turned on captions... didn't help. It looks like he says Mother's Committee on _______ , but the captions just say "Mother's Committee." Anyone have the script laying around the house? I would guess it was something like "Mother's Committee on Decency" or some such... and maybe the public was getting sick of the decency standards by that time, so they shortened the name after filming was completed. Did you notice Frank Cady, one of the politicians in the meeting at Reynold's house, was Sam Drucker, the shopkeeper in Green Acres, and Dick Elliot was Mayor Pike in the Andy Griffith Show. And, or course, "Doc", Fred Clark, was also Betty Grable's date in "How to Marry a Millionaire".
I just watched the DVD of “Flamingo Road” last night, and of course noticed that annoying jump in the dialogue also. I remember reading many years ago, before “Flamingo Road” was even released on VHS, that the negative of this film had shrunk because of improper storage. (In fact, it was noted by the author of the article that it was doubtful that “Flamingo Road” would ever be available for home video.) Bearing that in mind, I must say that a beautiful job has been done on refurbishing the print (the DVD looks great), but I wonder if the missing words in that line of dialogue were due to a bit of irreparable damage in the soundtrack because of the negative shrinkage.
I think you may very well be right. For those with a burning curiosity: Based on the book - I would guess the missing word in the film is "decency." In Robert Wilder's novel, on page 327, he refers to the group as the "Mothers' Decency League."
I watched what was said to be a 35mm print of this tonight and the exact same problem was there. So either the DVD was mastered off this print, or all the prints have this issue.