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)
Other mistake: Veeko has a hard landing on top of the elevator at the construction site. It's shown when the camera pans up to him, that the elevator doors are vertical scissor gates that open sticking out of the cabin, we see the actual door going up and being lowered to close the gates. Few moments later he is crawling with his body between the cabin and the floor and yet new workers get into the elevator without pushing the gate door up into his stomach. (01:15:55)
Other mistake: Veeko flips away from the descending elevator, is shown falling almost vertically on his back, and yet in the close-up behind him there's no elevator pit/outside of the building, but a solid inner part of the floor with people doing some construction work. (01:16:20)
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)
Revealing mistake: Brian Haley's stuntman launches himself out of the building by his own will in the sequence when the cart reaches the edge (he lets go off the cart handle before the impact and jumps right into 'the void'). (01:17:10)
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)
Plot hole: There is a scene setting up the nonsensical resolution of the plot, when the policeman recaps the various baby sightings. First; he already got 'fake' reports he chased, there was a scene about that, let's ignore the fact that certainly he would have gotten more like that and he conveniently for the plot lists just the few relevant ones. Second; the baby was kidnapped at 10 and the baby sighting on the bus happens "in the morning." Then the zoo sighting happens "at 3 o'clock." The construction site closes at 5 o'clock. Even forgetting the superior stamina of the 9 months baby that has been walking a whole day without a break, that's a lot of stretch for the actions as shown in the movie, in particular the time between the bus and the zoo; the bad guys would have been loitering in search of the baby for hours between the bus incident and the moment when he leaves the department store to get to the zoo.
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.