Numerous times throughout the film, snow is seen in the immediate vicinity, but in the distance, green grass is visible, as are trees with green leaves on them.
When Jack is killing the girl in the bathtub, she can be seen waving her hand in front of the window from the outside, but every time they cut back to her being attacked, her hands/arms are stuck inside Jack.
Manners confronts Frost, who grows icicle fangs and bites Manners' face. Manners is left disfigured and presumed dead. However, he returns in "Jack Frost 2: Revenge Of The Mutant Killer Snowman".