During the scene when Homer and Marge are talking in their bedroom after Homer is released from jail, the lights briefly flicker. Many fans believe this to be Hans Moleman-last seen being lead to the electric chair-being executed.
At the beginning of the episode, Marge's necklace is white. Later on it is her trademark orange necklace. The necklace Marge usually wears is a shade of red.
When Marge is cutting celery in the kitchen, she only moves the knife up and down, not horizontally, yet somehow manages to cut the celery into several slices. It is reasonable to assume that she was moving the celery horizontally, not the knife.
On Marge's first assignment for the Springfield Police Department she is told to patrol "Junkyville and Bumtown." Yet when she is walking down the street the clinic says "Junkytown Legal Clinic." This may just be the name of that specific clinic, not the same of the town.
Chief Wiggum's hair color changes several times during the episode, from black to blue and then back to black.
During the driving exercise, Marge is shown wearing a white shirt, but wearing a police uniform when she finishes.
When Barney is voicing his worries about their beer running out, the hair on his chest is missing.