That's the setup. Most of the rest of the movie consists of cartoon-style sight gags, as Baby Bink (played by twins Adam and Jacob Worton) fecklessly crawls through the city on an odyssey inspired by his favorite story book. While all adults (except for the kidnappers) somehow never notice him, Bink boards crawls on high rooftops, boards a bus, takes a cab, visits Marshall Field's, and goes to the zoo, where he is embraced by a protective great ape.
Before the movie is over we've even been treated to the venerable cartoon gag of Bink crawling out on an I-beam, high in the air at a construction site. And when, a little later, one of the bad guys hits the ground, he makes a dust cloud just like Wile E. Coyote.
If the action is inspired by cartoons, the three kidnappers are inspired by the Three Stooges. They're not really evil, of course, simply stupid and incompetent, as they allow the kid to crawl out of captivity and then somehow can't recapture him even though he's usually in sight.
John Hughes, who produced and wrote the movie, and Patrick Read Johnson, who directed it, are counting on one of the basic gimmicks of animated humor: Physical pain doesn't really hurt.
Characters can get slammed and flattened, but they pick themselves up, dust themselves off, and start all over again. The joy in physical pain here, inflicted mostly on the crooks, reflects the same comic taste that shaped the treatment of the burglar's in Hughes' "Home Alone" movies.
A closer look at cartoons reveals, however, that little time elapses between pain and payoff. One of the worst sequences in "Baby's Day Out" involves Mantegna hiding the kid under a coat on his lap, while two cops question him. Baby Bink finds Mantegna's lighter, snaps it on, and sets his crotch on fire. The hidden fire lasts forever, it seems, while Mantegna's face tries to mask the pain. Then the cops leave, Mantegna leaps up, his pants burst into flame, and one of his pals saves him by stamping out the fire - grinding his heel into the burning crotch, of course. The sequence was agonizing, but I didn't think it was funny.
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