While at her psychiatry stand and naming Chalie Brown's possible phobias, Lucy says, "How about cats? If you're afraid of cats, you have ailuroPHASIA.", If Charlie Brown were indeed afraid of cats he would have ailuroPHOBIA. Ailurophasia is, literally, "Speaking cat".
When Charlie Brown consults Lucy for psychiatric help, her sign (as read from the front) says, "The Doctor Is Real In". However, when seen from the side angle, the sign simply says, "The Doctor Is In".
During Linus's speech from Luke 2:8-14, he drops his security blanket when he says, "Fear not: for behold..." He continues the rest of his speech with the blanket on the stage next to him. However, in the long shot when he says, "And on earth peace, good will toward men," it's back in his left hand. Immediately after, when his speech in finished, he makes a point of picking his blanket up off the stage.
When Linus is making his speech Charlie Brown is behind him and to his left, and he has is not wearing his red coat. When Linus is briefly shown from his right Charlie Brown is in the background wearing his coat. When the shot cuts back to a front view the coat is off again.
After Linus makes his speech, he walks up to Charlie Brown and convinces him that what he said is what Christmas is all about. After that, Charlie Brown picks up the tree and starts walking out. However, when he walks past the other kids, Linus is within the crowd, despite the fact that he wasn't supposed to be there.
During the final scene, the Peanuts gang gathers around the little tree and begins to sing "Hark the Herald Angels Sing" (singing "Loo loo loo"). As everyone takes a breath, Pig Pen's head disappears briefly and Patty's orange dress (she's behind him) "pops up" to where his head used to be. Older VHS tapes have the mistake, newer tapes and DVD do not.
During the final scene, the gang is singing "Hark the Herald Angels Sing". Shermy, the boy in the yellow on the right side of the screen, disappears after the gang greets Charlie Brown. In Shermy's place is the boy in a blue coat who is still on the right side of the screen. So Shermy disappears and out comes a clone of the blue boy.