When he renders his judgment in the climactic sequence at the end of the film, Jugde Harper 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 of which this is a remake: At that time, the U.S. Treasury still issued a form of banknotes called silver certificates.)
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 car, however, Alberta's legs are completely covered by her overcoat.
Near the beginning of the film, when the drunk Santa falls off the parade float, you can see a sack full of presents on the back of the float. In the next shot, when people are lifting the sleigh off him, the presents have disappeared.
When Santa Claus 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 name in Italian is "Babbo Natale".
When Santa Claus 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, Santa Claus is referred to as "De Kerstman". "De Kerstman" and "Sinterklaas" act and dress differently, and have their own separate holiday.