It is quite obvious that the raining scenes at the end of the luau sequence are not real; they are superimposed over top of the original footage to give such an impression.
"Hawaiian Cruise" was the last installment of My Three Sons on the ABC Television Network to be broadcast as a repeat, as well as in black-and-white, on September 2, 1965, lowering the curtain on a half-decade run. Its switch to CBS - and color! - occurred a full 2 weeks later, in the exact same time period (Thursday @ 8:30 EDT).
The character name of the travel clerk (played by Olan Soule) is Edward Willis.