Factual error: At the time Amelie's mother dies, little Amelie is about 6/7 years old - you can see her standing in the church just before the tourist falls on her mother. Around the time Amelie leaves the house of her father, she is about 22 years old. However, the narrator speaks of a time-period of five years, which means Amelie would have to be around 15 years old when her mother died.
Continuity mistake: When Nino pulls back the photo booth curtain to reveal the bald "mystery man", the man's toolbox is on the photo booth stool. However, shortly before, we saw the legs and feet of the man standing in the photo booth, and the toolbox was nowhere in sight, and there was nowhere in the booth to hide it. (01:39:00)
Other mistake: Amelie only recorded a bit of the Tour de France. When you see it played on the glass man's VCR then there is a bit before she started recording that is being played.
Continuity mistake: After Amelie returned the box to the old man. The old man goes to a bar, Amelie is sitting close to him. She drinks 3/4 of her wine. Then the old man asked her "If she ever had kids?" She doesn't answer, but she gulps the same cup of wine, but this time it was full. (00:32:35)
Factual error: When Amelie see the plane crash on TV, that scene was set circa 1980. However, the plane shown was an Airbus A320, which was not introduced until 1987.
Answer: As far as I can see, Amelie is just trying to give him a view of the world, so he doesn't become entirely cut off.