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 the boy and the snowman first enter the boy'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.
Before leaving Santa's house, the Snowman points to the sky outside to indicate that the sun is coming up. Any location north of the Arctic Circle, presumably including Santa's house, would be shrouded in darkness around Christmas time, and would not have a rising sun.