When Monica reads the notes that David has written, the number of pages in her hand change between shots.
When the robots open the frozen door to the Amphib Craft, David's trousers are already wet on the left leg from the knee down. But when he gets out, they are dry and twice he slips on the ice and both times he lands on his left knee.
Teddy disappears from the dinner table between shots.
When we see the chef mecha scavenging for a new eye, he has no hat. But when we see him again in the cage, his hat is clearly a permanent part of his head.
One of the boys gets out of the swimming pool twice in different shots.
In the Flesh Fair, when the "nanny" robot is dissolved under the shower of acid, the acid was transported in and dumped from tin buckets. Any acid that acted that quickly on the mecha would have eaten through a metal bucket just as quickly, thus the worker who carried the bucket would never had had time to carry it to and make it up that ladder.
If the oceans froze, the water levels would have drastically receded, leaving Manhattan once again exposed.
The Antarctic ice cap, where most of the ice exists, has survived much warmer pre-industrial times. Even if all the ice caps melted and the sea rose due to global warming, the rate of rise would be very slow and land would still exist. Enough time for populations to migrate to higher ground, as populations have done in the past.
The Empire State Building is never seen, either the crew working on the the movie's CGI forgot to add the Building or it is possible that it might have just collapsed sometime before the movie's time period.
The World Trade Towers wouldn't be standing, for obvious reasons.
New Jersey is depicted as having tropical forest. This is due to global warming.
David malfunctions after ingesting food but suffers no discomfort at all from being fully submerged in water while in the pool. This is because he never swallowed any of the water.
Robots shouldn't blink, but David does when he is in the woods telling Gigolo Joe what he will do when he meets the Blue Fairy.
As the narrator describes the oceans, he mispronounces the word "anemones," reading it as "an-enemies."
When Henry asks David why he was going to cut Monica's hair, his lips don't match what he is saying.
In the orga-cannot-love-a-mecha dialog, in the reverse shots the mouth movement of does not always match what is said. You can see a closing jaw, yet the produced sound require opening your mouth, and vice versa.
Pre-cut face and a pulling cable is clearly visible when David meets another copy of him in the partially flooded Manhattan's Rockefeller Center and hitting him (it) with a desk lamp.
Much of the film's early action takes place in Haddonfield, New Jersey. New York City is subsequently shown to be under water. Haddonfield's elevation (81 feet) is lower than that of New York City (87 feet), and it is near both the Atlantic coast and a river leading to the ocean, so Haddonfield should be under water too.
The Swintons live in New Jersey, but Martin's prescription bottle is from a Los Angeles pharmacy. (This is visible briefly when the spinning turntable stops and before the bottle is picked up.)
At the end of the film David jumps into the water in downtown Manhattan and lands in Coney Island, which is in Brooklyn.
When the futuristic aircraft is approaching the former World Trade Center the towers are in the incorrect places in relation to where they are going. After passing them the craft approaches the Chrysler Building implying that they went north. However, back when they are approaching the towers the North Tower (the one with the antenna on it) is on the right and casting a shadow on the south, meaning its closer to the camera. The only way for this view to be possible is if they (the future robots) were heading east as the North Tower is further north than the south. This would mean that they are heading somewhere into Brooklyn not Midtown Manhattan.
It makes no sense that the aliens, who were capable of interstellar travel and controlling robots with their minds, could only make clones that last for one day. Humans can make clones that last for years.
The William Butler Yeats poem is misquoted on the door in Dr. Hobby's office. Dr. Know reads it "Come away, O human child! To the waters and the wild..." This is the correct line, and also what Gigolo Joe says as he reads it. However, the lines on the door read "To the waters of the wild".
"Carlo Collodi" is a pseudonym and Dr Know should have known that.