The idea of having the bath house workers clean the river spirit in the bath house came from an experience Hayao Miyazaki had (when he was younger) where he helped clean a polluted river, and one of the items that was removed from it was a bicycle. See more...
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Continuity: To the right of Kamaji on the wooden decking, there are two folded purple sheets on top of each other, clearly visible in the overhead shot when he yells "You sootballs got a problem?! Now get back to work!" However, when Chihiro and Lin leave and Chihro thanks Kamaji, when he says "Good luck," you can see that it is now a purple sheet on top of a blue sheet.
Continuity: When Chihiro talks to Kamaji about taking the train to see Zeniba, she says "Yep, I'll walk back along the tracks," and turns around, and the little mouse and bird are sitting on her left shoulder. It then cuts to a wideshot of Chihro walking over to Haku, but now the mouse and little bird have vanished from her shoulder.
Factual error: At the start of the film Chihiro's father slams on the brake to avoid the statue in the road and quickly stops. There are three pedals, meaning that this is a manual transmission car, but he only puts his foot down on the brake and doesn't touch the clutch. Whilst he would stop, there was not enough time for the car to stop as quickly and as smoothly as it did. The car would also stall out but it doesn't.