On a farm, Daffy waits for his new Dick Tracy comic book to the tune of Raymond Scott's song "Powerhouse". The mailman then arrives, and he receives the comic book. To the tune of the Poet and Peasant overture, he sprints to a corner of the farm and reads it. Then, he wishes to become Dick Tracy and then knocks himself out by accidentally punching himself.
He then imagines himself to be "Duck Twacy, the famous detec-a-tive." Ignoring a piggy bank theft crime wave, he goes into action when he learns that his own bank has also been stolen from his secure safe. He calls a taxi to follow a car but leaves without him ("Keeps them on their toes."). Daffy, at one point bumped into one Sherlock Holmes and told him he is working on the side of the street.
Daffy's search leads him to a tram with Porky as the driver leading to the gangsters' not-so-secret hideout, where he faces off against all the dangerous criminals in town: Mouse Man, Snake Eyes (spoof of B.B. Eyes), 88 Teeth (spoof of 88 Keys), Hammerhead, Pussycat Puss (who looks like Sylvester), Bat Man (a parody name of the real Batman where DC Comics is now owned by WB), Doubleheader (spoof of Tulza "Haf-and-Haf" Tuzon), Pickle Puss (spoof of Pruneface), Pumpkinhead, Neon Noodle (spoof of Frankenstein), Jukebox Jaw, Wolfman (spoof of the real Wolf Man), Flattop, Rubberhead, Ironman, and a host of other unnamed grotesques (the villains are obvious parodies of Dick Tracy's rogues gallery). He declares "You're all under arrest!!" The villains then roar at our hero and the chase begins.
The bad guys use well-known Dick Tracy villain Flattop's head (perhaps a Mount Rushmore-style variant) as an airstrip with planes taking off. Rubberhead "rubs him out" with his head as an eraser but Daffy appears at the door. Pumpkinhead meanwhile moves in with submachine gun blazing. Daffy tosses a hand grenade directly to Pumpkinhead's head, which becomes a stack of pumpkin pies.
After being chased about, Daffy eventually turns the tables on the villains and traps them inside a hallway closet. He slams the door shut on them and eradicates the group with sustained fire from a Tommy gun (which, if this were not a cartoon, would be a grim scene indeed, echoing the climactic scene from Warner's film The Big Sleep, released the same year).
He faces one last adversary, Neon Noodle (who survived because he is a mere neon outline with no physical "center" for Daffy to shoot), whom Daffy defeats by turning into a neon sign that reads "Eat at Joe's" (a standard WB cartoon gag). He then finds the missing piggy banks, including his own. He begins to kiss his bank, but since he is dreaming he doesn't realize that he is on the farm again, kissing a real female pig. The plump yet slightly curvaceous pig is rather smitten by Daffy since she believes he's trying to woo her with the barrage of smooches he plants all around her face while saying things like "I've found you at last!" He wraps his kisses up with a peck to the pig's little nose. So in an elegant female voice she says "Shall we dance?" and lovingly kisses him right in the mouth. Now wide awake, Daffy wipes the kiss away disgustedly and runs away. The lady pig says "I love that duck!" and laughs.
- When this cartoon aired on the Kids WB shows Bugs n' Daffy and The Daffy Duck Show, the scene of Daffy locking all the criminals in a closet, blasting them with his Tommy gun, and all of the criminals falling out in rapid succession was cut.
- Daffy's early line about Dick Tracy, "I love that man!" and the pig's closing line, "I love that duck!" are references to a popular catch-phrase of the time, "Love dat man!", said by the character Beulah on the radio series Fibber McGee and Molly. Clampett would use the gag again in his next and final cartoon at Warner Bros. Cartoons, "The Big Snooze".
- John Kricfalusi, the creator of Ren and Stimpy and fan/protege to Bob Clampett, named this as his favorite cartoon on the DVD commentary for Looney Tunes Golden Collection: Volume 2.
- In the Tiny Toon Adventures episode "New Character Day", there was a segment called "The Return of Pluck Tracy" where Plucky Duck is in the same role that Daffy had here. Here, Pluck Tracy had to rescue Shirley the Loon's aura (who is really Hatta Mari) from gangsters like Ticklepuss, Boxcars, Millipede Pete, etc.
- In 1994 it was voted #16 of the 50 Greatest Cartoons of all time by members of the animation field.
- When Duck Twacy takes a street car to the gangsters' hideout, the conductor is a thinly-disguised Porky Pig dressed in a driver's uniform and a handlebar mustache.
- Animation historian Steve Schneider said of this picture: "Bob Clampett's forever priceless "The Great Piggy Bank Robbery" is clearly a work of the highest cinematic poetry, for prompting the film's manic hilarity are a sequence of images that remain among the most indelible in cartoon history."
- This is the first Looney Tunes cartoon with a new opening and closing arrangement of "The Merry-Go-Round Broke Down", which would be used until 1955.
- Some sources erroneously credit animation by Robert McKimson, who had his own directing unit at the time this cartoon was in production.
- Daffy says "Sufferin' succotash" while waiting for his Dick Tracy comic. This line would eventually become the catchphrase of Sylvester, who also has a lisp in his voice.
- In the scene in which Daffy is seen through a door in silhouette as Duck Twacy, his shadow briefly morphs into Dick Tracy's trademark profile.
- In this film the WB shield doesn't zoom to the viewers, only the sound effect is heard. This error also occurred in "Kitty Kornered".
- An episode of Batman: The Brave and the Bold titled "Legends of the Dark-Mite" contains a sequence which heavily parodies the cartoon. Unlike when Daffy faces criminals which are parodies, here Bat-Mite faces actual Batman villains (namely Joker, Penguin, Riddler, Catwoman, Two-Face, Mr. Freeze, Mad Hatter, Catman, Polka-Dot Man, Tweedledum and Tweedledee, Killer Moth, Kite Man, Zebra-Man, and Tiger Shark). As an example, miniature Kite Man figures launch off the top hat of the Mad Hatter.
- This cartoon was the third cartoon in the a.a.p. package to bear that company's logo on a Cartoon Network broadcast since the return of Looney Tunes to that channel in 2009 after a three-year hiatus (with a five-year hiatus for the post-7/48 package), the first two such cartoons also starred Daffy Duck: "Daffy Duck in Hollywood" and "Nasty Quacks". The a.a.p. print of this cartoon aired on the 2010 New Year's Day LT marathon.
- This cartoon was also mentioned on an episode of Golden Book Video Killers where Daffy Duck was too scared after watching What Was That?
- This was the third cartoon and second Looney Tunes cartoon shown on Cartoon Network when the channel launched on October 1, 1992, just after "Rhapsody Rabbit".
- Daffy's line after falling into the trap door "Was that trip really necessary?" was a reference to the World War II slogan "Is this trip really necessary?" which discouraged Americans from doing non-essential travelling in order to save oil, gas and rubber (tires) for the benefit of the WWII soldiers fighting overseas. At the time the cartoon was released in theaters, World War II had ended.
- "Flat Top" is the only actual Dick Tracy villain depicted in the cartoon, but he is never explicitly named or labeled. He is shown launching miniature fighter planes of the top of his head.
- Warren Beatty wanted this cartoon to be re-released in theaters preceding his live-action movie Dick Tracy (1990). But Disney (who was making and distributing the film) refused.
- When the mailman delivers Daffy's mail, one of the letters is addressed to Rod Scribner, who was one of the animators on this short.