I liked the movie, character, and actress, but I could summarize a lot of complaints I've heard (almost none of which I agree with). I've heard complaints about Larson based on her evidently being a misandrist (thinking women are superior to men, the opposite of being misogynist), although most of the things that "prove" she is misandrist are taken out of context. I've also heard a lot about her not showing emotion, although that's largely the point of her character, as well as that her only emotion is anger.
Regarding the character, I've heard that she's overpowered, doesn't have a story arc, and is presented as perfect (the last two definitely aren't true, and that first one is based on how you define "overpowered")
Regarding the movie itself, the main complaint I've heard about it was that it was too feminist, with most people pointing to the advertising having "They need her" turn into "They need a hero" (taking the "her" from "hero"), which fails to separate the movie from the advertising, which are different, and the scene in the actual movie where she steals the creepy dude's motorcycle and breaks his hand, which most people (myself included) have a distorted memory of, it's actually not as big of a deal as many people think.
