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: Despite making the jump with Eddie from one building to the next, the two goons come out of the original building they jumped away from. (00:27:00 - 00:28:20)
Continuity mistake: When the two kidnappers realise the baby is drooling on them from the skylight, Mantegna in the shot from above is holding the pen in his right hand. It was in his left a moment earlier. (00:25:10)
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: 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: 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: 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.
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: The three guys look at the bus leave; Norby is biting his fingers and Veeko has initially his hand on Eddie's shoulder but (same shot) lowers it. Cut to the bus steering, and now Norby has both hands on his thighs and Veeko's hand is back on Eddie's shoulder. While technically they could have time to move their arms like that, they are meant to be "frozen" in shock in the same position and there's no logic in the change. (00:29:45)
Continuity mistake: After the credits, Cynthia Nixon is reading the story to the baby. When there's a transition between an establishing shot of the room and a close-up as she says "Baby Boo's nanny Henrietta says", her long bang in front of the left shoulder disappears. And a moment later, her right hand goes from the side of the book to the middle. (00:03:20)
Continuity mistake: Look behind Norby when he pries open the bus doors; a woman with a teal pantsuit is not exactly inconspicuous as she strolls along the sidewalk. A few cuts after (when he says "A little guy, about two feet tall") the same extra is recycled, walking in the exact same direction. (00:31:50)
Continuity mistake: When the mother and the nanny are rushing back to the room where the phony photographers were, the housekeeper is doing some cleaning in a part of the hall to the side of the door. The butler opens the double doors, and she is suddenly already in view, trailing behind the trio. (00:14:30)
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: Eddie falls from the roof and breaks his fall on a window-mounted air conditioner. In the close-up through the window, no cable can be seen behind Joe Mantegna's head (supposed to be there as he took it down with his crotch earlier), but it is there in other shots. (00:27:00)
Continuity mistake: When Brian Haley absolutely decks Joe Pantoliano with a smack to the back of the head, the delighted baby is shown in two close-ups. In the second he is not in the same spot (look at the cloth behind his head) and his hair is combed differently across the forehead. (00:17:20)
Continuity mistake: When the three stooges are about to jump from their hideout's roof, in the shot from behind Eddie has just one foot on the cloth placed on the edge of the building, while with the camera in front he has both feet on it, and Veeko's right foot fits too. (00:26:50)
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: From the kitchen table, Veeko tosses Baby Bink's storybook to Norby. He is tossing it with the back of the book on the left of the screen. When Joe Pantoliano catches a book tossed from stagehands, the book is turned the other way around. (00:20:05)
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)
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.