There are many ways in which Seven Psychopaths is problematic. But in most of those ways, the movie is also a direct attack on those problematic qualities in mainstream movies. (It would be difficult to have any sort of discussion about this movie without significant spoilers, so I'm not going to bother trying.)
For example, there are barely any women in the movie. They pretty much all die violent deaths. None of them have a particularly strong active role in the plot, nor are shown onscreen exercising any sort of agency.
When Hans calls Marty out on that point -- Marty being the writer working on the screenplay of the movie "Seven Psychopaths" -- Marty says something like "Life is hard on women." He's being obviously dismissive, and Hans is obviously unsatisfied. The audience, I think, is expected to be in on the point that mainstream media's treatment of women can't be called feminist or progressive just because screenwriters and directors say stuff like "Women are trivialized and objectified -- just like in real life! And that's awful," in interviews when they get called out on it.
The TVTropes article on Seven Psychopaths contains the bullet point: "Lampshade Hanging: Everwhere once they head out into the desert." Translated: "T.X. Watson loves this movie once they head out into the desert."
Billy is pretty obviously psychotic from pretty early on, though that mightn't have been very clear if it hadn't been for the title. But the reveal, when it becomes obvious to Marty that he's a psychopath, was incredible. "Do not burn neighbor's flag." Cut to neighbor's flag, burnt almost entirely off.
I love Billy's character -- I think it's a great depiction of what life is like for most psychopaths. He wants to fit in. He wants to be able to live in normal life, with friends, and peace, and comfort. But he can't, because there just isn't that thing in him that compels him to act against his own, immediate interests. He doesn't have any empathy.
So he tries to reason his way around it: "People have a right to fly a flag." But reason is just barely good enough to get him to behave mildly normally in public. He makes it obvious that reason alone isn't a substitute for a moral sense -- he can't stop himself acting in his own shallowest, most immediate interest if he's doing anything else at all. If he's choosing not to do something because he's reasoned that it's wrong, that has to be his activity. Sitting down, looking out the window, actively, constantly choosing not to burn down his neighbor's flag.
It's obvious that psychopathy isn't a two-way street here. Billy can't empathize with the audience. He can care what we think of him, and he can work to earn the perception he wants people to have. But he can't ever actually see himself the way we see him.
But we can empathize with Billy, and we do. We empathize with all the psychopaths, because often as hard for a non-psychopathic person to not care as it is for Billy to not burn his neighbor's flag.
So, yeah. I recommend this movie. Its reflections on media, on psychopathy, on the nature of character flaws, are all compelling and engrossing. I kinda think I want to own this one.