The only thing that many people criticize her is her personality. One minute she was slamming Britney Spears and swore that she'd never dress like a music hore, selling her body instead of her music, the next minute she's become another Britney Spears, or as she thinks, "a punk version of Britney Spears and a more mature" of herself. She then sings songs like "Hot" and "Girlfriend" and wears revealing clothes.
She often claims that she is not a pop star but in fact she is. Basically, her songs are just pop songs with some rock beats.
Since her third album, her style changed to more pop, but she thinks it's girly punk. She now tries to act gothic, and have launched a fashion line of clothes and perfumes(one called "Forbidden Rose").
However, despite that many think she's fake and arrogant(she pretended having baby just for fun), there are still many, most are teenagers, love and support her. She is commercially successful.