During the movie's climactic scene with Joe and Simon in the hospital.
In the second baseball scene, Joe is sitting on the bench next to one character with the number 8 and Simon, who is on Joe's other side is also number 8. Two players on the same team would not be the same number.
In the scene where both boys are in the school, just before breaking in Father's office, the dog is licking Simon's glasses, this leaves a wet smeared mark. In the next shot, the glasses are clear again.
In the Christmas Pageant scenes, Miss Leavey is seen pulling down on the rope that raises or lowers the kid playing the angel. By pulling down on the rope, the kid should go higher. But when Miss Leavey pulls down on the rope, the kid is lowered as well.
When Rebecca Wenteworth is walking towards the baseball diamond, she is looking behind her and waving. When she gets hit in the head with the ball, it's on the wrong side of the face. She should have been hit on the left side of the face.
The fateful Christmas in question is in December 1964, but a news item on the radio reports a speech given by President Kennedy, killed a year earlier.
Throughout the entire film, Simon can be seen wearing a hearing-aid (behind the ear). These were developed in the 1960's, however the model seen in the movie was not available until after 1964.
Joe and Simon are at the Police Station, the music playing is "Nowhere to Run" by Martha and the Vandellas, which was first released Feb 10, 1965. The film was based in 1964.