Continuity mistake: The first time we see Bink crawling out of the big lady's bag, in frame you can see Veeko's legs, feet up, but he has not been knocked out yet. (00:33:40)
Continuity mistake: Baby Bink is making his way inside the department store after getting pushed by the revolving door. POV shots have him walk on a decorated portion of the floor, but in the side views he keeps creeping on plain tiles. (00:34:40)
Continuity mistake: Ronnie Lee drops the microphone and the bad guys notice the baby getting in frame; they turn around twice across two shots, in the second of which Joe Mantegna has his right hand up, while he had both arms down in the first. (00:37:50)
Continuity mistake: In the overhead shot of the baby in the middle of the road in front of the zoo, the road is lit evenly, while in the shot just before you could see half a lane being in full sunlight. (00:42:55)
Continuity mistake: In the close-up of the three idiot kidnappers getting their feet crushed by a passing van as they stand in the middle of the street, their order in the line is wrong. The leftmost person is wearing boots, so it's supposed to be Veeko, who is in the center in the other shots. (00:44:10)
Continuity mistake: The three kidnappers run after the baby who got into the zoo; they jump over the shrub between two benches, but the leftmost bench is occupied by a lady who disappears between shots. (00:44:20)
Continuity mistake: Veeko is trying to pry Baby Bink away from the gorilla cage pulling him by the shoelace. In the side view the floor of the cage is littered with half eaten fruit, but in the close-up all of that is gone. (00:47:35)
Continuity mistake: Veeko screams in Norby's face when he touches the hand pounded by the gorilla; Norby has both hands in front of his mouth as reaction, but they disappear in the reverse shot. (00:48:50)
Continuity mistake: Veeko sits on a bench to scream in pain after the gorilla's less than friendly actions. In the background you can see the cleaning cart with the mop placed against the brick wall. In other angles the mop is against the doorframe instead. (00:49:10)
Continuity mistake: After being tossed across the building by the gorilla, Eddie is stuck between bars with the arms being positioned differently between shots (right arm down/right arm up in the front view). (00:53:00)
Continuity mistake: Baby Bink crawls out of the monkey building with his shoes unlaced, but they tie themselves up perfectly off-camera for the next scene. (00:56:30)
Continuity mistake: Baby Bink spots a donut left on the girder by the construction worker. The donut turns around (going by the bitten part) and moves (going by the way it sits on the napkin and how much of it is on one side or the other) between shots, repeatedly. (01:08:30 - 01:09:15)
Continuity mistake: Norby rips a bit of Veeko's pants from the right leg; when we see a close-up of Pantoliano, the filament popping in frame from above comes from the left side (if it's a shoelace and not part of the torn pants, Veeko's boots were not unlaced). As he falls, we see for a moment Veeko's feet and there's no torn fabric dangling. (01:13:50)
Continuity mistake: As Veeko tests the milk's temperature on Joe Pantoliano's bald head, the baby's hand position is out of continuity in the close-up compared to the shots before and after (off/on chest). (01:16:50)
Continuity mistake: Eddie reaches the "little ball of grief" and promises he's not gonna crawl away. The baby has conspicuously shown drool on his chin as he coos in response, but it's gone a moment later. (01:17:45)
Continuity mistake: When the construction site guard wakes up, in the aerial shot he's in the sun, while in the close-up is in shadow. (01:22:25)
Continuity mistake: When the parents finally do find the baby, in the close-up of Bink you can see the left arm of the old soldier who found him first; he was leaning on the armrest at an angle before, but he's resting perfectly horizontal now. (01:26:45)
Continuity mistake: In the ending, Bink reaches for a book (hint of the sequel never made, "Baby's trip to China"). The book is sticking out more in the close-up, easier for the baby to grab.
Answer: It might have taken a while for them to find the keys to the crane as well as figuring out how to operate it. Once they did, they could get him down.