(Around 43 minutes) When Bryan & Dorey go on their date he is wearing a plain blue wool scarf but later on, at the ice rink, it is silk with stars on it.
While Bryan is giving his final statement, Susan is seen sitting away from Dorey in one shot and cuddled up next to her seconds later.
Near the beginning of the film, when Tony falls off the parade float, you can see a sack full of presents on the back of it. In the next shot, when people are lifting the sleigh off of him, the sack has disappeared.
Kris raises his walking stick to strike Tony. In one shot he has his hand near the crook handle. In the next shot, the crook handle strikes Tony's head.
When Jack and Alberta have dropped Kris off at the old folks' home and Jack is returning to the limousine, you can see Alberta's crossed legs through the open door. When Jack enters the limousine, however, Alberta's legs are completely covered by her overcoat.
When Kris tells the little girl his name in other countries, he states that in Italy his name is "La Befana", however, that is the name of the kind witch that flies around filling stockings on January 6th. His Italian name is "Babbo Natale".
When Kris tells the little girl his name in other countries, he says that in Holland his name is "Sinterklaas", however, that is the name of another December holiday figure. In Holland, he is referred to as "De Kerstman". They act and dress differently, and have their own separate holiday.
In the "We believe" list is Ironworkers Local 542. There is no such branch in New York state. The other union reference (Teamsters Local 237) is correct.
An important plot point of the movie is that Kriss's trial takes place on Christmas Eve in New York City. This means that he should have already have delivered presents to every country which is GMT+7 or ahead, as it is already Christmas Day in those countries. In short this means that Children in Countries like Australia, New Zeeland, the UK and Europe have already had their Christmas Day ruined.
In the Thanksgiving Parade scene, the trees in Central Park are seen budding for spring (the scene was shot in April).
Shortly after Kris is acquitted, the camera cuts to an aerial view of Central Park which is resplendent in green. But this is supposed to be Christmas Eve when all the trees should be bare.
The first day of the committal hearing is a Thursday. It is then continued on Friday. At the end of that day, the Judge states that he will deliver his verdict at noon the next day. This would make it a Saturday, and US courts are not open on weekends.
While in Kris' room at the psychiatric hospital, a reflection of a crew member can be seen in the side of the shiny porcelain sink.
When Judge Harper renders his judgment in the climactic sequence at the end of the film, he mentions that the $1 bill on which he found the words "In God We Trust" was issued by the Treasury of the United States. In fact, current U.S. banknotes are issued by the Federal Reserve Banks, not the Treasury. (Note that this error does not apply to the original 1947 film: at that time, the U.S. Treasury still issued a form of banknotes called silver certificates.)
When Chris takes the stand, he asked the Judge about his grandson. The prosecutor should at least have raised the question about how they knew each, if not outright ask the Judge to recuse himself.
(Around 61 minutes) Judge Harper says the hearing is set for "Thursday morning, 9am". AM means in the morning so he should have said either "Thursday morning, 9:00" or "Thursday, 9am".