While the puppy Hachi travels from Japan locked in a crate, his collar disappears and then mysteriously reappears.
When Hachi digs under the fence to follow the professor he is clearly covered in mud as we see him on the other side of the fence, but when we see him on the platform he is clean again.
When Cate awakens Parker, who has fallen asleep watching Game 6 of the 1996 World Series with Hachi, the footage shown on the television is of then-Yankee catcher Joe Girardi running out his run-scoring triple in that game. Presumably it's late, and Parker and Hachi had been watching the game quite a while for Parker to have fallen asleep, but Girardi's triple came in the 3rd inning. It's also questionable whether Parker, who's depicted as an avid Yankee fan, would fall asleep during a World Series-clinching game.
The puppy has obviously grown several weeks between its departure from a monastery in Japan and being found at a train station presumably less than a day after.
After the reporter takes the photos, the Japanese professor Ken reads his article "Faithful Dog Awaits Return Of Deceased Master -- Hachiko looks for professor seven years after he died of a heart attack." He then visits Hachi at the station and says to him (in Japanese) "It has been a year, hasn't it?" Clearly only a year has passed since Parker's death, not seven, which is also apparent from the relative youth of Hachi at the time of Ken's visit.
When Hachiko has moved in with Andy, Michael and Ronnie (still a baby), he is shown laying on the floor, while Ronnie collides with the dog repeatedly in his baby walker. In the first shot showing the walker from the side, the baby is absent from his walker. Cut to a master shot showing baby Ronnie in the walker, followed by another shot of the walker colliding with Hachi, similar to the first which shows now the baby's legs.
When Hachi sees Lucky, the poodle, at the station, the video is obviously running in reverse when Lucky goes back to her owner as the leash mysteriously levitates back in to the owner's hand.
1:03:19 - The tip of the microphone is visible in the screenshot with Cate Wilson (Joan Allen).
When they confront the skunk in the backyard the scene ends with the wrong assumption that skunks spray backwards which is untrue. Skunks will stand on their front paws, arch their backs and spray forwards over their heads.
The commuter train that Parker rides is equipment (locomotive and cars) of the Providence and Worcester Railroad. However, the Providence and Worcester does not operate regularly scheduled passenger trains and did not at the time the movie was being made.
The Wilson's TV remote is an RCA universal DVD available remote that was not available at the time.
When Hachi brings the ball to Parker at the station, while Parker opens the door, the reflection of the camera is visible in the window of the door.