- In the film's opening scene, "Mr. Smith" collects his suitcase full of stolen top secret government documents. As he leaves, the airport employee who handed him his suitcase phones "Mr. Jones", who picks up a bag of golf clubs as part of his disguise and quickly pursues "Mr. Smith". As they exit their taxis and "Mr. Smith" follows a deliberately roundabout route to the hotel to try to lose "Mr. Jones", the latter, frustrated by the weight of his golf clubs, takes several opportunities to throw away the clubs a few at a time, until he is left with just one in the bag by the time he reaches the hotel. Throughout the chaos of the rest of the film, he still has the golf club bag with one club in it at all times, and no-one seems to find it the least bit peculiar.
- At the banquet for the Congress of American Musicologists, Judy has completely charmed Mr. Larrabee and the other musicologists (except for Hugh Simon) by pretending to be Howard's fiancée, Eunice. As they sit down to dinner, with Howard and Judy either side of Mr. Larrabee (to Hugh's frustration), Howard asks to speak to Judy under the table, and they both scoot their chairs back so they can get their upper bodies under the table. Moments into Howard protesting Judy's presence at the dinner, Mr. Larrabee also bends under the table to see if everything is all right, then Hugh bends under the table in an attempt to kiss up to Mr. Larrabee, and then the other musicologists at their table - all of whom are smitten by Judy - bend under the table. Cut to the head waiter looking at this strange group of people with their heads under the table and asking another waiter what sort of wine he is serving them.
- The scene in Howard's hotel room after the banquet is a hilarious comedy of errors.
- First, as he starts changing into his pyjamas, he hears a voice in the bathroom - and is horrified to find Judy taking a bubble bath. She points out that if he calls the police, it's more likely they'll arrest the man with his trousers around his ankles than the woman in the bath. He tells her to get out of the bath, but quickly changes his mind as she stands up covered only in soap bubbles.
- As Howard tries to fend off a phone call from Eunice, still angry at him for pretending not to know her at the banquet itself and wondering why she heard loud noises in his room, Judy loudly declares that she'll get dressed now; Howard tries to cover by saying that it's a film on television about fighting WACs, and switches on the set. Eunice is not convinced, and declares that she is on her way. Howard calmly tells Judy that he has no choice but to jump out of the window. As she tries to pull him back, she tears his pyjama trousers down the back.
- Eventually, with some effort, Howard persuades Judy to hide on the window ledge, wearing nothing but a towel. As Eunice tries to find the owner of the voice she heard over the phone, she demands to know why Howard has run a bubble bath, as he never takes bubble baths. Howard feebly explains that the water came out of the tap that way. Fortunately for him, Eunice doesn't broaden her search, or she'd have noticed Judy's clothes still hanging on the back of the bathroom door...
- Meanwhile, the room service food that Judy ordered while in Howard's room arrives. Eunice orders Howard to switch off the television, but he succeeds only in turning the volume up to full before the knob comes off in his hand. She tells him to unplug it, but it's plugged into the wall by a cable instead of a standard cord, and Howard's attempts to pull out the cable cause a shower of sparks that sets fire to the curtains and his suitcase.
- All the while, "Mr. Jones" is also on the window ledge, still carrying his golf bag, trying to avoid being seen by "Mr. Smith" during his act of counter-theft; when Judy grabs his leg in an attempt to clamber back onto the ledge, he is so startled that he smashes through the window into Howard's room, showering the floor with broken glass. As he sees the fire, he joins Howard in hopelessly trying to extinguish it with the contents of the room service tray; they are soon joined by hotel detective Harry and receptionist Fritz, the would-be jewel thieves. As the room burns, the room service waiter continues calmly laying out the food on the tray and checking that it matches the order. A brigade of firemen arrives, but they can't work out which room is on fire and succeed mostly in falling over each other and their equipment. Judy, standing at the shattered window and still only wearing a towel, looks at the chaos and innocently chides Eunice for being in her fiancé's room before they're married.
- The climactic chase scene. Howard and Judy flee Larrabee's party with all four suitcases - one of which is Howard's and one of which is Judy's, but they have no idea which and no time to open them and find out - as Harry and the fences who were going to buy the jewels pile into their car (with Eunice, Hugh, and Larrabee held at gunpoint), "Mr. Smith" flags down a taxi, and "Mr. Jones" flags down a passer-by in a convertible. Mayhem of the most hilarious sort ensues:
- Howard and Judy commandeer a grocery delivery trike while its rider is busy making a delivery, with Judy pedalling and Howard perched on the box at the front (into which they have stuffed the four cases). Eventually, they reach a hill with a very tall ladder at the bottom, at the top of which a man is hanging a banner advertising Keep San Francisco Clean Week. Meanwhile, two workmen are carrying a large pane of glass across the road. Somehow, the trike and the three cars manage to keep missing the ladder and the glass, even as the trike cannot get to the top of the next hill and rolls backwards and turns down a side road, with the cars still in pursuit (smashing up a parked VW microbus as they turn around, to the shock of the unfortunate owner)... until finally, the ladder is clipped by the final car. The banner hanger grabs onto the banner, which tears off and sends him arcing towards the glass, which shatters into powder.
- Howard and Judy ride the trike through a parade in Chinatown featuring a dragon costume, which they end up wearing. As they shoot through a red light, they cause a seven-car pile-up, one car in which ends up covered by the back half of the costume after it tears off, and the remaining part of the costume proceeds to knock over an entire residential street's worth of garbage cans, sending them rolling toward an alarmed pedestrian.
Judy: Where are we, I can't see!
Howard: [smiling thinly] Well, there's not much to see, actually, we're inside a Chinese dragon.
- After getting rid of the trike and the dragon costume and donning other costumes stolen from a costume shop, Judy suggests she and Howard steal a VW Beetle parked outside Saints Peter and Paul Church as a newly-married couple exit the church toward the car. She doesn't bother to tell him that she can't drive until they're already on their way (the wrong way down a one-way street - as she calmly points out, "We're only going one way!"). She accidentally switches on the wipers, then when Howard switches places with her and asks her to turn them off, she ends up switching on the radio (which is playing appropriate fiddle-based chase music) and the sprayers.
- The four cars drive through sand being emptied out of a dump truck, causing the workman waiting at the back of the truck with a spade to throw down his tool in resignation. Moments later, all four cars drive through newly-laid wet cement (in Howard and Judy's case, first in one direction and then the other when they see the other three cars bearing down on them), causing the workman who has just laid the cement to throw his tool down in a rage and jump up and down in the ruined cement.
- Judy tells Howard to turn down what she is sure is a road. It turns out to be the giant stone staircase in the middle of Alta Plaza Park, but with the other cars hot on their tail, they have no choice but to drive down them, as do their pursuers.note As they flee the park, Howard complains that he can't see through his dirty glasses; Judy removes them to clean them, making Howard's eyesight even worse. But when she replaces them and he can actually see where the car is going, he changes his mind about wanting to see it and throws his glasses out of the window.
- The audience - and Judy - see what Howard was afraid of seeing: a departing ferry for Sausalito. Judy has Howard accelerate towards it, saying "We can make it!" while he protests. And as the car soars gracefully toward the water, missing the ferry completely, she amends her declaration to a deadpan "I don't think we can make it." The other cars soon follow them into the bay. Within seconds, an assortment of police cars also shows up, crowding the end of the dock so much that two policemen end up falling in as well.
- After the damage they have caused, the occupants of the four cars are naturally arrested and brought to court, and more laughs follow.
- The judge is on many forms of medication, and as the assembled defendants shout over each other and Howard's attempt to explain on everyone's behalf just keeps getting more confusing, he pops more and more pills and takes more and more tonics.
- After the mess of defendants are brought in, the judge asks the arresting officer to explain the charges:
Judge: Officer! What are these people being charged with?
Arresting Officer: It's kind of hard to explain, Judge.
Judge: Give it a shot.
Arresting Officer: Well, we picked most of them out of San Francisco Bay.
Judge: Entering the country illegally?
Arresting Officer: No sir, they drove in.
Judge: Into the country?
Arresting Officer: Into the bay.
Judge: Ah, that's better. Unauthorized use of public water. [begins writing down a list of charges]
Arresting Officer: Mostly in stolen cars.
Judge: Aha, that's grand larceny.
Arresting Officer: Then there was a shooting...
Judge: That's assault with a deadly weapon.
Mr. Larrabee: They broke into my home.
Judge: That's breaking and entering.
Mr. Larrabee: [indicating Eunice] And brought her with them forcibly!
Judge: That's kidnapping.
Eunice: They tried to molest me.
Judge: That's... unbelievable.
- Howard volunteers to be the group's spokesman, which goes about as well as one would expect for an Absent-Minded Professor. As if the fact that he only occasionally specifies whether his use of "she" refers to Eunice or "Burnsie" (i.e., Judy) and/or refers to both of them as "not my wife" while clarifying that one is his fiancée but the other is not isn't confusing enough, he then causes a Who's on First? routine between himself and the judge:
Howard: It gets kind of complicated now. First, there was this trouble between me and Hugh.
Judge: You and me?
Howard: No, not you. Hugh.
Hugh: I am Hugh.
Judge: You are me?
Hugh: No, I am Hugh.
Judge: Stop saying that! [to bailiff] Make him stop saying that!
Hugh: [as the bailiff grabs him] Don't touch me, I'm a doctor!
Judge: Of what?
Judge: Can you fix a hi-fi?
Hugh: ...No, sir.
Judge: Then shut up!
- Finally, the judge notices Judy hiding under a blanket, and since Howard has indicated her without naming her throughout his account of events, he asks her to explain things, since she seems to be the source of the confusion. As she emerges from the blanket, we discover just why she was trying not to be seen:
Judge: You! You in the blanket! You seem to have caused all this trouble. Exactly what have you got to say for yourself? [Judy slowly lowers the blanket; the judge is stunned] ...Judy!?
Judy: [sheepishly] Hello, Daddy.
[Judge Maxwell's bench completely collapses]
- And our heroes on the plane at the very end:
Judy: Love means never having to say you're sorry. [Bats her eyelashes]
Howard: ...That's the dumbest thing I ever heard.