Factual error: When Clark speaks to Jor-El for the first time in the Fortress, Jor-El says "I will have been dead for many thousands of your years..." Fine in theory - Baby Kal-El travelled to Earth at above light speed so time passed differently for him. However, as such, wouldn't Jor-El have seen Earth as it was thousands of years ago? Which also makes there a problem with all the things Kal-El was taught during his voyage to Earth, as Jor-El references Einstein by name, for instance, and he would not have existed at the point when Jor-El sent him to Earth.
Visible crew/equipment: As the Tin Man gets to the end of his song, he's dancing in front of three mirrors. If you look past him as he's centered in the middle mirror, you can see the camera lens looking out of the canvas at him.
Continuity mistake: As Max is carrying a birthday cake out of the kitchen, the candle blows out as he walks. But the candle is suddenly lit again when the camera angle changes, as he walks into the living room.
Continuity mistake: The rabbits have a close encounter with some rats in a shed on the cemetery. A spade falls over. In the next shot the spade lays in a wheelbarrow.
Visible crew/equipment: When Gene is on top of the coaster at the amusement park, you can see a cameraman below filming.
Continuity mistake: When Tony and Tia are being driven to their hotel, the same footage is shown behind them a few times e.g. A truck turning off the road when their driver shouts at an overtaking driver and a few minutes later when he shouts at the same driver again.
Factual error: In the 1953 sequence when the headmaster is driving Fiona and Paul home, the yellow car parked in the road is a Vauxhall Viva HC, which didn't start production until 1970.
Continuity mistake: When Stella is put into the machine to revive her after being frozen, her head is tilted to the right when she goes in, but is tilted to the left when the shot changes.
Other mistake: When the Fellowship takes a rest after escaping the snowstorm, Gandalf and Aragorn begin arguing about which path to take from there. When Aragorn suggests the Gap of Rohan, Gandalf protests, saying, "That will take the Ring too close to Isengard," followed by "and Aruman" instead of "Saruman." (00:55:00)