As you write reviews, you eventually come up with various scoring systems. You start with some implicit understanding of what makes a good anime, distill this understanding to specific mechanics of the show and attempt to figure out how these mechanics are executed. And then you assign value to this execution and come up with a score. Most of the time, this score properly reflects your overall opinion of the series.
Sometimes, however, a show comes along that simply straight up ignores all the storytelling rules that you made up in your head. With no visible effort, it tears down all your preconceptions of what makes a good anime and forces you in a situation where you need to choose one of the three paths. You either forfeit any reviewer pride you have and just enjoy the show, without trying to analyze it. Or you lie to yourself that it is bad and you didn't like it all that much and there is no way that a show that ignores all those nice rules in your head can be good (in which case you write a disparaging review, trying to make the show fit your preconceptions). Or you learn about all the new mechanics (or new ways to use the old mechanics) employed in the show, defensibly arrive at a mark that corresponds with your true opinion of the show and come out as a better reviewer.
I'm a fan of the third approach, and Seitokai no Ichizon Lv.2 allows to do just that.
Video
The visuals of this show give mixed impressions.
On one hand, they decidedly lack complexity.
All the action takes place in a very limited amount of very simple locations, with kind of simple backgrounds. All the characters are drawn in a decidedly similar way - you'll be distinguishing them by their height, hair style and color more than anything else. Which creates a small bit of confusion as the cast expands beyond the original few in the student council. The OP sequence is completely generic. The ED sequence is ... well just sad. The only part of the visuals that shows any attempt at weaving any sort of complex visual pattern are the school uniforms.
On another hand, the visuals are delightfully simplistic.
Backgrounds don't draw attention to themselves and allow you to focus entirely on what the characters are doing. Simplistic character design allows to translate the character's feelings in direct and simple ways, which certainly allows for higher level of character empathy than a lot of other significantly more visually elaborate shows. The only "frilly" part of the visuals - which are school uniforms - are really milked for everything they are worth in the scenes where the viewer needs to be given the impression that the females in this show are both beatiful and sexy. Furthermore, unlike the true ecchi shows, Seitokai no Ichizon does not show huge open cleavages and half-screen butt-shots, showing elaborate lacy underwear. Instead, the show's simplistic style gives you just enough to kick-start the imagination, while still leaving it enough room for imagination to run completely rampant.
In my opinion, a noticeably more effective tactic.
So, while the show's simplicity does at times work against it, i still feel the need to point out that this simplicity is both well justified in terms of viewer experience, and does actually confer it a unique sense of style. You won't mistake Seitokai for any other show, and that alone warrants a good mark, despite the drawbacks.
While there are shows out there that do "simple" better (Lucky Star and School Rumble both come to mind), and it is certainly true that Seitokai's visuals are probably closer to "average" than "amazing", simply because of the truly limited toolset that gets employed. However, the amount of pure expressive mileage the show manages to squeeze out of that limited toolset is really nothing to scoff at. 7/10.
Sound
Sound doesn't stand out in any good sort of way. It doesn't really stand out in any bad sort of way, either, but I personally found OP/ED annoying. Therefore 4/10 here.
Story
The story is weird.
On the surface level, it has a ridiculous almost-eroge-level plot, happens in a very small amount of locales, with a very small amount of people, doesn't have any big sort of conflict in it, is very much disjointed and seems to spend a great deal of time maintaining a weird sort of relationship status quo. You wouldn't be completely wrong in saying that the story here is 8 episodes' worth of bland humor situations between two episodes of somewhat "serious" story development. And i'm certainly not kidding when i say "bland", the humor here is definitely nowhere near the level of the aforementioned Lucky Star and School Rumble.
However, the story still has the capacity to grip you and glue you to the screen. This is done through two mechanics.
First, there actually is an underlying conflict that gradually gets resolved as the series progress (and this is what makes Seitokai Lv.2 story way better than season one). The main protagonist is actually, episode by episode, realising his goal of making all the girls around him happy. He even has a time limit in the form of graduation, which is the moment when he loses contact with any of the girls he has weak connections with by the time it comes. If you can get behind that goal and the stress of the time limit, i'm reasonably certain you'll love the story :)
Second, the story has no qualms whatsoever about breaking the fourth wall and openly talking about who is the main character and who is not, what kind of story they are in, and how to make it better for the viewer. In fact, an entire second episode is spent discussing this topic, and in later episodes it is then revisited at the show's convenience. The interesting part is that it doesn't seem awkward at all, but rather serves as a great vehicle towards deepening the interaction of male protagonist with surrounding girls, and thus works towards resolution of underlying conflict.
In short, the story in this show is just like the video. It is simplistic (to the point of being hurt by the simplicity) in the sense that there is just one single story thread here. But this story thread is really and truly milked for all that it's worth, through the use of all available storytelling mechanisms, both orthodox and not. It is a story not for everyone, because it's scope is really fixed on that one single thing the protagonist is trying to achieve. But if it is for you - it will be both easy to get into and genuinely entertaining. 7/10.
Characters:
Basically, the characters are cliched and poorly presented (occasionally completely indistinguishable from one another). This is a bad thing, which would normally warrant a 1/10 rating from the get-go.
Much like the video section and the story section, the creators didn't really bother with elaborate backstories for pretty much everyone, with the exception of the single back story that is relevant to the central conflict.
The catch here is that it is not the case that the creators forgot to make their characters interesting, or failed at doing it despite trying. No, the creators actually made a conscious decision to outright forfeit any pretense on originality from the get-go, which they reinforce through characters openly discussing other character's stereotypes in the aforementioned fourth-wall-breaking scenes.
What the creators are truly interested in is character development of the main protagonist, as well as growth of his relationships with the various girls (and corresponding development of the girls themselves). And, let me say this, every single bland joke scene works towards that goal. Trust me, i watched it a second time, just to confirm. It is really quite uncanny. I honestly can't name a single series which managed to get this much development out of an almost completely one-dimensional cast.
This effect is achieved by having the characters openly acknowledge their one-dimensional nature, do it with perfect acceptance and even with a good amount of glee, introducing a second dimension to the protagonist through the story conflict, and then just letting it all unfold.
Now, despite all that, i can't say that the character job is really amazing, or even particularily good. Whereas simplistic style worked reasonably well for visuals and story, it seems you just can't get away with that level of simplicity in characters. They do get almost immediately boring for the viewer that doesn't get immediately sold on the core source of their development. Even if you do, building up a convincing relationship from such poor basic building blocks takes quite a good amount of really poor basic situations, just to fit the blocks together to form the initial framework from which the true relationship can arise. This is the source of all the bland humor :(.
Furthermore, a couple of characters that should have been more prominent in the story, simply get forgotten, with all of their development pretty much voided in terms of potential impact. Which is sad.
Normally this cast of absolutely poorly executed (and occasionally throwaway) cliches wouldn't warrant more than 1/10. However, i think that the sheer development work that is done in this show brings a fail up to at least "B-". That's 5/10.
Value:
This show's value is like the value of being able to do arithmetics in your head, despite living in the modern world of scientific calculators and heavy-duty calculus.
On one hand, it is almost completely worthless, not worth more than 1/10. What this show does can be done more effectively by adding simply a wee bit more complexity on any of it's simplistic parts.
On another hand, it has amazing value, 9/10 or higher, because it takes you back to the basics, both in terms of production and experience, reminds you just what exactly you can do with just those basics, and puts everything that people do with more advanced tools in a much needed perspective.
Being torn and truly unable to decide between 1/10 and 9/10 in this category, i'll settle for 5/10.
Enjoyment:
Enjoyment of this show ties heavily into your ability and desire for two things
a) Sympathise with the main protagonist
b) Let your imagination run wild, working off the minimal things provided by the show's creators
For me personally, both of these things clicked, so i enjoyed it way more than the modest scores in other categories would have you believe.
However, if harem stories are not your kind of thing, and also if you like your imagination pre-processed by elaborate artists working with high-end graphic computers, then you should probably stay away.
Since this is the one category that allows for my personal bias, i'll go ahead and give it a 9/10 :P