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Continuity: In the scene where Hanna shoots up the interview room, including two soldiers, she gets blood spattered on her face and forehead. The blood is there throughout the subsequent chase but disappears when she is standing in the clean room motioning the doctor to get in the locker (most noticeably it's gone from her forehead). She didn't wipe it off because it reappears just after she shoots the man in the locker when she's stealing the medical report from the desk.
Factual error: in the film Hanna talks about there being 8 planets. the film also suggests that Hanna and her father have been living in the forest for her whole life of 16 years and her only knowledge coming from books. it was 1996 when the government had any traces of Hanna's father, so that makes the film set in 2011/12. so if she has only ever got her information from books published before she was born, she would still think there are 9 planets, because Pluto wasn't officially named a dwarf planet until 2006.
Other: In the beginning, Eric reads to Hanna from an encyclopedia. He first talks about the blue whale. Hanna asks him about music and then he turns two pages further and reads the article about music. This is impossible if he was looking up the whale under the letter "W", because he then would have had to turn a lot of pages back, instead of further. Also, had the entry been under the letter "B" from blue, it would have been further than 2 pages. He could not have been looking up the word "Mammal", because there would not be more than the mentioning of the name "Whale" under that description, and not an entire explanation plus picture of this animal like in the movie. If he would want info on the Whale like the info he read, he would have had to look it up under the letter "W", this is true in any encyclopedia.