In the opening scene the patrons of the casino Lupin and Jigen just robbed try to pursue them. Key word being "try."
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 crack this troper up. 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 international authorities to drop his investigation of 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.
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: *Face Palm* He's such 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?
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 you dare go dying before I can arrest you!"
When Jigen and Goemon carry the phony Lupin and interrupt the wedding, Jigen is wearing vampire fangs for no particular reason.