These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Sayonara, Zetsubou-Sensei
Awesome Music: The soundtrack varies between hauntingly beautiful orchestral pieces as season main themes, great piano minuets for Nozomu, and the rather light, silly fare used for the rest of the show.
The opening themes all use a mixture of punk vocals (for the main singer), J-poppy backup singers, grunge guitar and (for the fourth OP) soaring piano melodies. The ending themes are an appropriately crazy mix of styles that manages to mesh, from swing jazz to surf rock to punk-infused cabaret.
Also, Kurayami Shinjuu Soushisouai. Made even better by the fact that Itoshiki's voice actor does the vocals, quite well too!
Acceptable Targets: Frequent targets including pervy otaku or NEET guys, immigrants, and China "a certain country" whose constant spying on Japan goes unacknowledged by the government for political reasons (North Korea gets a similar treatment).
Fridge Logic: Lampshaded once during the whole "thank-you thievery" bit. During a rainstorm, Chiri gives Harumi a drink pouch under an umbrella (Harumi is holding it initially). Harumi then holds the drink pouch in one hand and a manga volume in the other, and Chiri has her hands at her side, visible. No one is holding up the umbrella.
"Funny Aneurysm" Moment: The last picture of Chapter 16, "The People Are At The Breaking Point", depicts the cooling tower of a nuclear power plant cracking and saying "kaboom". This predates the Fukushima Nuclear Plant crisis by 5 and a half years.
From a few chapters later...
Nozomu: To get a stable electrical supply, we have unstable nuclear plants!
And then there's the "promotional manga" informing the public on the use of spent nuclear fuel in manga Volume 4, supposedly put out by a Paper-Thin Disguise for the Tokyo Electric Power Company (TEPCO) (complete with Maria briefly turning into a marionette with visible strings). TEPCO of course became the most notorious utility company in Japan (and perhaps the world) after the 2011 Fukushima meltdown.
Hilarious in Hindsight: In response to the Shizuo and Izaya pairing, Ryogo Narita, the author of Durarara!!, said that he couldn't say anything because he likes to ship Harumi and Chiri. One chapter shows that Harumi is indeed a Shizuo/Izaya fan. Although it's difficult to say which came first without a proper time reference.
Ho Yay: Every time fanservice occurs, all of male students give attention to the girl in the fanservice scene, save Jun Kudo, who is generally reading. Maybe he is really concentrated on reading it... but some of the official art makes it hard to believe that, especially art like this◊. Not to mention Kafuka can possess him too because of the blood transfusion he received from her. It's hinted that Jun was the incarnation of Kafuka that Nozomu consumated their marriage with. Fujiyoshi would approve.
Starting with Volume 5, the English edition of the manga goes from being translated by Jason Thompson to David Ury. There are now much fewer annotations for the references and cultural notes, and the wording of all the character's catchphrases has changed. It's definitely a mixed bag, though. Vol. 5 doesn't have nearly as many dense references, and a lot more of them are directly explained in the text; the really unfamiliar things are still explained. The original translation of Zetsubou-sensei's Catch Phrase wasn't exactly like what we're used to, but changing it to "I've lost faith in [whatever]" is a major downgrade. The new translation also downgrades Kafuka's blatant Cloud Cuckoo Lander-ness, although Chiri is still just as much of a psycho. Volume 9 saw Ury being replaced with Joeshua Weeks, who isn't as good at including explanations of references right in the text but at least makes sure to use the phrase "I'm in despair" more often than Ury.
As far as the anime, if various comments within Zan and the No Man's Land/Bangaichi OVA are any indication, Japanese fans are saying this about Zan, specifically how the animation quality has dropped rather noticeably and it lacks Shaft's trademark quirks that were so prominent in the first two seasons. THEM Anime Reviews complained that the pacing of Zan is lacking what made them fall in love with the series in the first place.
It's also like tripping into drugs without taking any.
The Untwist: People seem to make a big deal about Kafuka's real name being An Akagi. The series kind of gave it away in numerous scenes.
Values Dissonance: Or rather, cultural beliefs dissonance. Nozomu is Squicked out by the Christmas holiday because he was born on November 4 and thus follows the still-prevalent Asian belief that the average human gestation period is 10 months and 10 days...thus he thinks he was conceived on Christmas. It's even worse for Kageru, since he was born on December 24 and thus believes he was conceived on Valentine's Day—two romantic holidays in one stone.
The Woobie: Maria, who woobifies herself and even makes Nozomu pity her.
Then the whole class end up wanting to protect her. Even Chiri. Sometimes.
Abiru Kobushi both subverts this trope and plays it straight, in that, on the one hand, all of her injuries are actually the result of her animal abuse and therefore entirely deserved, while on the other hand she was fooled into thinking her teacher returned her feelings, a notion which he coldly disabuses her of.
The author himself. Be sure to read his notes at the ends of volumes.
I think I'm creepy. I just can't stand any part of myself. If I went to a picnic and saw my ugly face reflected in the lake, I'd just jump into it. If I went shopping and saw my ugly figure reflected in the show window, I'd bang my head against the glass and cut my throat with a fragment. My TV is always on. That's because if I turned it off, I'd see my ugly reflection. On sunny days, I have no desire to leave the house. Even my shadow is ugly. I'm an ugly manga child who'll never see the day when I become a swan. I changed the lightbulb over my sink to the lowest wattage.
Poor Minami is stuck working several dozen part-time jobs to pay off her unfaithful husband's debts, and she just accepts it all. Aw...