At the Siblings Anonymous meeting, Roger Clinton explains that he got upset watching footage of his famous brother Bill on the History Channel making his 1993 State of the Union Address to Congress. There was no State of the Union address in 1993 as Bill Clinton had just become President and the traditional speech never takes place during an inauguration year.
When Fred is attacked by Santa's Secret Service upon his initial arrival to the North Pole, a patch of snow remains stuck to his face. Not only does this not melt any from his body heat, but the patch changes places several times during subsequent shots.
During the "intervention" scene, after he has broken free of his wrapping paper and tape bonds, the amount of gift wrap still stuck on Fred varies. Specifically, a piece appears and disappears on the left breast pocket of his shirt.
After Northcutt kills the power, and Fred and Willy are "flying blind", Willy consults a map and says they're near "longitude 38.25..." and shouts for Fred to "take a left!" When Fred takes the left turn, they're in Tokyo. The Longitude of Tokyo is 139 degrees, 46 minutes East. 38.25 East is the Longitude of Matui, Tanzania.
The narrator tells us: "it's a little-known rule of sainthood, but when you become a saint, you freeze in time, eternally ageless. The rule applies to the family of the saint and the spouses, as well." Of course, there is no such "rule" in real life; sainthood is conferred upon deceased people only.
Willy tells Fred that they have 10 hours to deliver the presents. Based on the world sunset/sunrise times on Christmas Eve/Christmas Day, they would actually have up to 29 hours, the points closest to the North Pole being in darkness the longest. Moreover, the delivery sequence has Fred traveling to spots that are not in darkness at the same time.
Willy tells Fred that they have until 5:38 AM sunrise "North Pole Time" to deliver the presents. As The North Pole is in darkness at Christmastime, there is no sunrise. Moreover, as the lines of longitude converge at the North Pole (and at the South Pole), there is no "North Pole Time", at all; researchers in the Arctic and Antarctic use the time zone associated with their research stations.