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.