It's been a few years since I watched any full episodes, but I can recall a few of these clips from memory, so someone who's better-versed with the series than I should be able to fill in any holes.
The shot of Francine answering the phone is used more than once during the series, but probably comes from "Stop Dragon My Cat Around".
The sequence where Speedy is running, only to have Polly and Guido's faces pop up in front of him, is sourced directly from the Japanese intro, and doesn't come from any particular episode.
Guido accosting the girls on the beach comes from "The Terror of Prisoner Island"; I'm pretty sure the shot of him getting hit in the face with the soda can comes from "No Talent Guido".
The old turtle comes from "Stop Dragon My Cat Around".
I'm not certain, but I think Speedy being drowned by the squid comes from "The Terror of Prisoner Island".
Speedy stepping on Polly's tail, and her reaction: Samurai Charm School, maybe?
The Cats running from the missile comes from "Underground, Underwater, and Undercooked".
Guido waving his arms above his head comes from the sequence where he and Speedy steal each other's pizza in "Stop Dragon My Cat Around".
Big Cheese singing probably comes from "Those Transformin' Felines".
The ending shot of Speedy falling off the bridge and into the water definitely comes from an episode, but I can't remember which one offhand; it might be "Speedy's Double-Time Trick".
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