When James comes downstairs, there is a pendulum swinging in the grandfather clock. When he is going outside the pendulum is gone.
When James goes outside to see his snowman, it has just chimed midnight, but when he returns to bed after visiting the North Pole, his clock says 11:35.
When James gets up from bed on the first night his bedside clock says 8:00 but the grandfather clock says 12:00 (approx 5 min 40).
When James and the Snowman leave the kitchen to go upstairs the grandfather clock says 8:05 again (9 min 06).
After the Snowman comes to life and first enters James's house, the cat is not lying in front of the fireplace. A moment later, the cat, sound asleep, is lying in front of the fireplace.
When James and the Snowman look at the motorcycle from the window, there is no snow on the tarp covering it. When they go outside to ride the motorcycle, there is snow on the tarp.
When James is turning the kitchen light switch on and off to show the Snowman, the switch always remains in the same position.
The snowman was so large he wouldn't have melted overnight.
When James and the Snowman are flying to the North Pole, they fly over some penguins which are not found in that region.
James and the Snowman are in southern England and fly over Brighton and towards the Brighton Pier - this is heading south and Father Christmas lives at the North Pole.
Before leaving Father Christmas's house, the Snowman points to the sky outside to indicate that it's almost sunrise. Any location north of the Arctic Circle, presumably including Father Christmas's house, would be shrouded in darkness around Christmas time, and the sun would not rise.