(CNN)"Green Book" won the Golden Globe for best comedy or musical on Sunday night, which would normally mean turning the page toward the Oscars. But hurdles remain for a movie that not only could be categorized as a drama but which has produced more off-screen drama than practically any other contender in the current awards season. Sunday's victory has seemingly invigorated the movie's Academy Award chances, perhaps more so than the Globes' drama winner, "Bohemian Rhapsody." But it has also renewed questions about the extent to which criticism and questions about the movie's veracity have undermined those hopes, or if it can weather them.