Captain Henderson at the beginning, as Sherman begs him for a chance to repair Sea Tiger rather than just scuttling her at the dock:
"What's it take to make you realize you've been sunk?"
Holden's introduction. Sea Tiger's crew are busy with the repairs. The enlisted men are in dungarees, the officers and chiefs in khakis, all of them greasy and filthy. Holden's dress whites practically sparkle. He clearly doesn't fit in. The scene ends with Sherman assigning Holden to supply duties and giving him a slap on the back that leaves a black handprint on his pristine uniform.
Log entry by Captain Sherman: "Sighted tanker, sank truck."
Some of the debris used to convince the USN destroyers that they weren't Japanese was some of the extra lingerie from the nurses. The look on face of the sailor who retrieved a bra (which happened to have been Crandall's) was priceless.
Made the subject of a great line when the Sea Tiger finally reaches Darwin: "We may be pink and coming in by the grace of a woman's brassiere, but by God we're coming in!"
The catcalls and whistles Sea Tiger gets from the other American ships in port just rubs in the embarrassment further, until Sherman shuts them all up by running up the American flag.
Also, the look on Sherman's face as he makes the request over the ship's interior communication system seals the absurdity of the idea.
As the Sea Tiger lurches out of port, the native witch doctor they brought in to perform a blessing ceremony pulls off his mask, watches for a moment, shakes his head and comments "They'll never make it", speaking in American-accented English.
The base commander at the beginning of the movie confronting Lt. Cmdr. Sherman about the items missing from his base.
Capt. Henderson: Mister Sherman, I want my wall back! (made while pointing at a large hole in the corrugated metal wall)
Holden telling Capt. Sherman how nervous he is about their first dive, only to be told that they're already submerged. Followed by this exchange:
Sherman: Well, if we can't [motions upwards], we [motions downwards].
Capt. Sherman: "Ensign Stovall. Henceforth, you shall refer to the 'casino' as the 'supply depot'." (Holden got the replacement parts for the Sea Tiger by running a combination pawn shop/casino where Army soldiers would trade stolen Army parts for casino chips, and then lose in the rigged games).
For that matter, Ensign Stovall in general. While he seems to be a fairly competent officer, he has a bad habit of making remarks toward Holden's antics which get on Sherman's nerves.
The look on Lt. Reid's face when she opens the door to the head, and we hear the pig Holden stashed inside grunt at her. Made even better by Holden smirking at her from the door to his cabin and Sherman's explanation.
Sherman: Yep, they're drafting everybody these days.
And she's so unable to process what she just saw that she walks away completely blank.
Sherman's gradually becoming Not So Above It All over the course of the movie, culminating in his amused reaction to Holden paddling after Duran in a lifeboat when she's angrily swimming away from him after he revealed he's engaged.
Also Duran's enraged comment as she storms off: "He's engaged to the Super Chief!"
Pretty much every mention of "Seaman Hornsby".
At the end, Sherman turns toward the Sea Tiger as it sets out. The music sets up a sort of "sailing into the sunset" kind of feeling. Then the No. 1 engine backfires.
Before that, Crandall, now Sherman's wife, arrives and crashes into Sherman's car, causing its front bumper to hook to the back of a bus. Sherman's aide chases the bus down, although Sherman himself takes it in good humor.