My first impression of the anime is that I really enjoy the minimalistic art style and animation. The use of colors and empty space in the panels (as an example, at 3:15 and 4:35, below) really give pop at the appropriate moments. Almost every background has moving animation, and there are very clean lines and vivid colors used for the backgrounds, which adds to the minimalistic feeling. I also thought that the use of shadows and darker colors to denote who was in the foreground and background was quite clever, and a very simple way to give depth to the scenes.
I also noticed that screentones were sometimes used in lieu of the standard cell shading - that, too, also added character to the style. The minimalism also does not preclude subtlety and complexity in the art style - almost every scene features a subtle lighting. For example, in the classrooms, you have the light shining in from the windows and from the hallway, even if the windows themselves are not in the panel.
I think I would have appreciated more variety in the character templates. All of the faces of the students looked the same, with only the hairstyle differing.
The sound effects, soundtrack, and voice acting were done superbly, in my opinion. All of the music corresponded well to the scenes (especially the more comic scenes in the classroom). Some of the sounds were actually pretty subtle, like at 12:31, when Fuura-chan shifts a little bit, and you hear her clothes rustle. Another great example of the use of sound effects was at 15:53, where they had the sound of the coins falling onto the ground with a black screen. Rather than animating the coins actually falling, they did the sound, then showed the coins on the podium.
The OP and ED were quirky but a lot of fun, and definitely fit in with the theme of the anime. The animation of the ED sequence was very beautiful - I saw lots of bits and pieces of traditional Japanese culture flitting around in the panels. That was on top of the old-style Japanese painting look that we could see in some panels.
I laughed the nod to the classic appearance of "birds flying through the sky" or "boats sailing through the water" in most anime OPs and EDs, occurring midway through the episode.
The political satire was wonderful! Haibane's example of even Mt. Fuji being named after a corporation with money was an excellent example. The number of jokes in the background and in the lines (such as on the chalkboards) were hilarious, though I didn't quite understand some of them. And then, of course, there was also Arai-sensei's comment of "How troublesome; what if he comes every day?" I'm pretty sure this is a reflection or a satirization of contemporary Japanese society, perhaps of how depression is generally viewed. I'm not 100% positive about that, though it does seem to make sense.
The puns in the character names were wonderful, especially that male student who is often overlooked. When I rewatched the episode a second time, I noticed that his face was rarely seen in its entirety; it was often covered by another person's face, and when Chiri-chan and Fuura-chan are talking about the school becoming a spa, his body was blacked out into a silhouette, while the two girls were in full color.
All in all, a very enjoyable first episode. I'm looking forward to seeing what happens with the students, the nurse, and with Zetsubou-sensei.