Factual error: When Arriety and Spiller are rescuing Peagreen from the bottle, Arriety introduces Peagreen to Spiller. But later on when her parents show up and she introduces Spiller to them, she also introduces Peagreen to Spiller again.
Other mistake: At the beginning, when Pod is climbing up the table, he does it in seconds. There's no way he could have gotten up that fast.
Plot hole: How could Pod have been sure that Pete would have all the things he needed, when he is preparing to rescue Peagreen from the milk bottle?
Other mistake: When Arrietty and Pea-Green slide along the power line, they go pretty far. They would have hit a post and gotten electrocuted.
Revealing mistake: Whenever there is a bird's eye view of the town, you can see that the far backgrounds are paintings.