After the boardroom meeting when Miles knocked Buddy over onto the floor and the picture fell off the wall, in the next scene the picture is back up on the wall. Also, Buddy is sitting down in an opposite position from the last scene when he got knocked down on the ground.
At the end of the movie when Buddy is reading his story to a group of children he says aloud that he "passed through the seven levels of the Candy Cane Forest, through the sea of TWIRLY SWIRLY gum drops", however the book from which he is reading clearly reads that he passed through the sea of "SWIRLY TWIRLY gumdrops". The previous two times he recounted the story, once to Walter, Michael, and Emily at the dinner table at their first meeting and then to the mail room guy in the mail room, he referred to it as the "sea of SWIRLY TWIRLY gumdrops".
In Central Park, while trying to fix Santa's sleigh, we see Buddy through the trap door. But in the long shot, as the sleigh rises off the ground a few feet, Buddy has disappeared. This happens several times in the scene.
In the beginning of the boardroom scene when Miles Finch is listening to their book ideas, his little black book full of story ideas moves back and forth from his left hand to his right hand when switching camera shots.
When Buddy is at the apartment having dinner with the family, the coke bottle is near Michael's right hand. When Buddy goes to drink the coke it is right next to him. He never asks for the coke to be passed.
When Santa moves the sleigh while Buddy is putting on the turbine engine to get away from the Central Park Rangers, Buddy flails, making it obvious that he is lying down on a softer padding than the floor.
After Buddy was arrested for assaulting the store Santa, he was let out pretty easily. In real life, Buddy wouldn't be released out so easily, as when he was booked at the jail, the NYPD would have been suspicious of the fact that he had no identification and no background (of course, if Buddy insisted he was an elf from the North Pole, the police would have probably thought he was insane and committed him to an asylum).
Santa tells Michael that just telling people he exists won't work as that would destroy the belief in Christmas Spirit so when he flies over the heads of all the people by the entrance to the park his sleigh should crash not fly faster.
When Michael is reading from Santa's list, he recites the names as they are listed. Suddenly, when given a name to "look up", he says "D" and flips pages looking for "D" as if the book is in alphabetical order. However, the names he already read are in no particular order.
When Buddy rides the revolving doors when he first comes to New York, he runs to the curb to throw up in the street trash can. You can see two people on the left waiting for the signal to start walking.