While Randolph is driving Sheldon through New York City, the trees outside the car look green, and people walking around are dressed fairly lightly. This is obviously during the spring/summer. However, when they arrive at their destination in New Jersey, it is snowing very hard, and the large amount of snow on the ground indicates it was snowing for a long time.
When Randolph gets upset over the picture of Sheldon and Nora, the picture he shows to Angelo is different from the one he originally sees in the magazine.
The shot of the dead body in Chinatown appears to have been flipped - the Chinese characters reflected in a pool on the street are not reversed.
When Catherene Keener throws a Frisbie at Sheldon's head it comes out of her right hand spinning clockwise, but in the Frisbie point-of-view shot it is spinning counter-clockwise.
During Smoochy's "Step-Dad" song, the young, bored-looking little girl over his left shoulder repeatedly appears and disappears.
On Buggy's sniper rifle, a laser's line isn't visible. Just the dot. Its line can only be seen if it is in smoke, fog or a thick gas.
As Sheldon runs off the ice to chase Burke Bennett, he is wearing hockey skates. In the theatrical film, it seems like the skates disappear by magic, but the DVD shows him removing the skates in a deleted scene.
Sheldon is arrested at the Nazi Party in New Jersey, but booked at a NYPD station which is in a different state.
When Nora talks to Sheldon Mopes/Smoochy ('Edward Norton'), she accidentally calls him "Ed".
Sheldon says that he was born on the day Sesame Street (1969) premiered, 11 November 1970. In fact, it premiered on 10 November 1969, which was 366 days earlier.