Character mistake: During the intro, Rukia says, referring to the Hollow's sound "I can hear it's loudass voice." Unnecessary vulgarness aside, it's "its", not "it's."
Character mistake: In the fight against the monster in the park in chapter 1, Rukia says that you must be willing even "to sacrAfice your own life."
Other mistake: Whoever did the English localization doesn't believe in commas (often long sentences go by without any), but sometimes errs on the other end of the spectrum. For instance, the intro of the game says; "Maybe it's because we're entrusted with the live of the living, but for as long as I remember." Full stop. It breaks the sentence, that continues in the next screen. The whole translation is full of examples of random punctuation throughout the game.