In this episode, Bender is shown as a baby on the conveyor belt, but in another episode, he was "born" fully grown.
Maybe Bender's memory doesn't go back that far.
During the episode, the professor states that Bender's oil leak is caused by a fatal defect. Although it is never mentioned about again in the episode after that.
When Hermes and Bender enter the Bureaucracy building, when the man stamps the paper, he only stamps it 3 times. However, in "How Hermes Requisitioned His Groove Back", it is revealed that you need to stamp the paper 5 times.
However, maybe the person who stamped the paper 3 times was fired off-screen.
The rules could have also changed.
The scene after Hermes and Bender return where Hermes returns Planet Express to its former state the fire that Hermes is shown shoveling paper into is layered over Leela and Fry.
When Bender and Hermes go to the physical files room, the button to open the door switches from the left to the right side of the door.
The computer in Inspector 5's hacienda disappears and reappears during the scene.