When the globe explodes and credits fall everywhere, the credits of the animators who worked on the title sequence can be seen.
The cast members who are listed "in alphabetical order" are actually listed as such: Milton Berle, Sid Caesar, Buddy Hackett, Ethel Merman, Mickey Rooney, Dick Shawn, Phil Silvers, Terry-Thomas, and Jonathan Winters.
Then some hands (presumably the characters themselves) move their credit to the top of the list, causing a squabble and shuffle to occur.
The final order is Silvers, Rooney, Berle, Winters, Merman, Hackett, Terry-Thomas, Caesar, and Shawn.
The opening credits are a sequence of gags all related to a globe of the world.
The final cast credit of the opening credits occurs when a hand unzips a zipper along the "World's" equator and shows (beneath a pair of eyes): "& Alyce Wittenstein"; and below that (in much smaller font): "& a few surprises".