I think Dylan has always dealt in stealth humor. For some reason he has this persona of dead seriousness, as if he were not capable of anything more than grim protest songs.
This is a protest movie without a doubt, and I think a really valid one. But it finally puts his sense of irony up front where it can't possibly be missed.
One example I just love: Jessica Lange is meeting with TV network executives, and they're yelling at her for not being able to come up with a better rock star than "Jack Fate" (Bob Dylan), telling her he's completely irrelevant and nobody cares about him. Meanwhile, there's a prime-time TV schedule on the wall behind Jessica Lange, and the sitcoms are named after Dylan songs: "Jokerman", "It's Alright Ma" ...