In the opening scene the security staff of the casino Lupin and Jigen just robbed try to pursue them. Key word being "try". The Streamline dub scores points for humor at the end of that scene, when the security staff is reeling from their failure. Out of the blue, as a lone wheel rolls slowly over to one of the broken cars, one security guard yells to his partner, "Where did you idiots learn to drive, anyway?" The Manga Entertainment dub instead opts for a Precision F-Strike to highlight the comedy, with one of the guards heard exclaiming "Son of a BITCH!" in the background.
The Manga Entertainment dub adds some extra dialogue to the scene where Lupin and Jigen, in disguise, cross the border into Cagliostro. Lupin introduces Jigen as his dad to the border guard, and Jigen later says to him, "Dad!? I don't look that old!"
Lupin's (successful) attempt to reach Clarisse's tower, especially when his impromptu long jumping skills come into play.
Some of the lines from Streamline's dub are amusing. Such as when Jodo's shadows burst into the motel room and Lupin asks "Hey, what is this - a tour group from Hell?"
Zenigata is told by Interpol to drop his investigation of Count Cagliostro, as he has too many "friends" in high places due to the extent of his counterfeit ring. So when Fujiko invites him to join Lupin in crashing the wedding, he eagerly agrees, charges right into the heart of the operation and makes it quite clear that he's making fun of his superiors by "discovering" the printing presses making counterfeit bills. On live television. Broadcasting worldwide.
Zenigata: "Oh NO! What Have We Here? Those look like Printing Presses! Mmm, and What Do I See Over There? Oh my, these are Yen! Could they be COUNTERFEIT?" Random diplomat: *facepalm* "Lord, he's a bad actor..." Zenigata: "There's fake money of All-Most Ev-Er-Ry Nation! I came looking for Lupin, but discovered a Crim-In-All plot! Oh, what to DO??"
It's even funnier in the original Streamline dub, since Zenigata doesn't even try to hide the fact that he's lying about his "accidental" discovery and STILLmakes a production of it anyway:
Zenigata:(in mock surprise) "Well, what do we have HERE?? Look: PRINTING PRESSES! What could they be printing I wonder...? Hm... let's take a look."
(pretends to snoop around)
Zenigata:(with armload of counterfeit bills) "Why it's money! COUNTERFEIT! Well, what do you think about that?"
foreign emissary:(facepalming) "We'll never cover this up..."
Zenigata:(blinks innocently) "Can you believe it??"
When Lupin and Zenigata first run into the heart of the counterfeiting operation, they call a truce until Zenigata can bring the operation down. Lupin offers to shake on it. Zenigata almost does so, but pulls away at the last second in a way that could almost be defined as Tsundere.
... That's pushing it.
Pretty much any scene with Zenigata is this. Another special mention goes to when Lupin is injured by a bullet, Zenigata screams this gem:
"LUPIN! Don't even think about dying before I arrest you!"
When Jigen and Goemon carry the phony Lupin and interrupt the wedding, Jigen is wearing vampire fangs for no particular reason.
Lupin himself was playing up the creepy factor by pretending to have been resurrected from the dead, "representing the deceased of the catacombs", there to claim the bride. Goemon's traditional choice of dress and concealed eyes in this instance already give a ghostly vibe, at least to a Japanese audience, but Jigen's suit would not have been so creepy by itself, so he either thought of wearing the fangs himself or Lupin convinced him to do it. In either case, he quickly loses the fangs as combat becomes imminent and they are never seen or mentioned again.
After Lupin escapes the castle with many injuries, he wakes up several days later and angrily says how he needs to eat a lot of food so he can recover quickly. Cut to him gorging himself until he literally turns green and his host asks if he needs a bucket.
Jigen: (as Lupin passes out) He says he's full.
(In the subtitled version, Jigen's line is that Lupin says he wants to sleep now, which is just as funny.)
When a massive fight breaks out at the wedding, Fujiko (there in disguise as a reporter covering the event) cheerfully gives a running description of the events while casually beating off soldiers that come near her with a wrench. At one point a soldier comes in from behind to attack the camera man. Still giving commentary, she pulls out a gun and shoots the soldier.
During the iconic car chase in the beginning, Lupin has to suddenly swerve when a huge truck appears in front of him. Amusing enough already, but made better in the 2000 English dub with Lupin yelling "OH, SHIT!"
When screening the movie to audiences, two moments that never fail to get a large laugh are the funny little sound-effect the statue makes when it spits out the Polaroid photos, and the way the masked assassins shuffle out in two perfect arcs in Clarice's bedroom.
Lupin and Jigen fighting over the pasta.
In most versions save for the Streamline dub, in which this scene depicts Jodo calling for reinforcements, as Lupin and Zenigata head for the Count's autogyro Jodo is being yelled at by the Count for failing to stop them from wrecking his printing presses, and Jodo then calls him out on Skewed Priorities and informs him of what Lupin and Zenigata could be doing next.
Cagliostro: You idiot!!! Jodo: This is no time to be yelling at me! They appear to be going for Clarisse! We have to stop them!
During the opening credits, Jigen is clearly relieving himself while he and Lupin are waiting on a passing train at one point.