I love when japanese criticize their own country, that's VERY MUCH NEEDED in the manga industry
If you look far and wide, you'll find them. In the manga by Kanzaki Yuuya I translate, there's a good deal of criticising the Japanese police and aspects of life in Japan.
Psychiatrist Yowai is a good take on the stigma of mental disease in Japan.
Stateless was unfortunately dropped by the scanlators, but it deals with how harsh the life of unregistered immigrant children is in the country. And by reading Tetsuya Tsutsui's works, one would think Japan is a crossing of a third-world banana republic and a bureaucratic dystopia. Oh, a tip of the hat would also go to Kimizuka Chikara's works, which deal in a no-nonsense way with bullying (as in, not for revenge porn purporses), criminal stigma and other themes.
What I
don't see in manga is direct criticism of the political system. Leaving aside whether it
merits criticism, you're hard put to find examples outside of sci-fi dystopias (because in these, it's not "real" Japanese politicians, but cartoon villain, alternate-world versions). People would probably point you to
Akumetsu, but by the time I dropped that one around chapter 30, it read more like a tragic hagiography of Junichirou Koizumi. Same for
Sanctuary.
Destroy and Revolution got close to the real thing, but ultimately vindicated the system.
If you want to see scorched-earth, pillaged-temple criticism of one's own country's system, you'd have to go for manhwa. From what I've read so far, Koreans are
far more cynical about their political system than the Japanese about their own.