When Kumiko calls her Mother in the middle of the night and tells her she couldn't sleep, it should have triggered some reaction from the mother. Because of the time difference between Minnesota and Tokyo (14 hours), it is never nighttime in Tokyo when it is in Minnesota.
In one scene, the police officer and Kumiko watch her Japanese copy of "Fargo." Region 2 DVDs do not work in Region 1 DVD players.
When she is visiting Paul Bunyan and Babe the Blue Ox, that is in Bemidji, MN which is located in Beltrami County. The Sheriffs car that pulls up says Tyrrell County on the side which doesn't exist in Minnesota.
Kumiko visits Musashino Place, a public library in suburban Tokyo. The library did not open until 2011.
Earlier in the film, a soapbox speech of an opposition politician is heard about how he is going to stop nuclear plants from operating again. Nuclear power became a major national issue only in the wake of the 2011 Fukushima disaster, and a Tokyo politician would not have spoken about it before.