Continuity mistake: 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 mistake: After pulling the rope to let the herbal water in, Chihro falls off of the side of the bathtub, onto the floor, and you can see two brooms leaned up against the side of the tub. Then, when No-face drops the herbal soak tokens, there is a wide shot of Chihro, and the brooms are gone.
Continuity mistake: In many closeups of Haku (like near the scene where he gets chased by paper) he has green eyes. But when he wakes up (in the scene with Zaniba turns Bou into a mouse), he has brown eyes.
Deliberate mistake: When her father jumps on the brakes, they lock up, even though the car is supposed to have ABS, which is supposed to prevent this from happening.
Continuity mistake: 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 (a pedal e-brake would be positioned differently), 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.
Plot hole: When her father is taking the "shortcut" he somehow doesn't need to shift gears even though he has a manual transmission. At the speed he was at he should be in at least 2nd gear.