Story - It's really difficult to describe a show based on only a few episodes, but Mitsudomoe doesn't really need a full season's worth of episodes for that. The anime is gag driven, much like Azumanga Daioh. Each episode works as a standalone one, divided into multiple mini gag-based plots. That's not to say that there is no long term plot throughout the series, because there is. The story revolves around a male teacher, who begins his new career teaching a middle school class that contains the troublesome Marui triplets. There is also a clumsy school nurse that he falls in love with at the beginning. This love progresses, if you could even call it progress, as the episodes go on. Primarily though, the show is about the triplets and their teacher getting into all manner of hilarious circumstances, often involving the classmates and the school nurse. Beware however, since Mitsudomoe is adult humor driven much of the time.
Art/Animation - The first thing you might notice is that the art is reminiscent of Azumanga, particularly the heads. Unlike most of the anime released, it does not rely on the more realistic design approach, instead opting for the super cute. This suits Mitsudomoe perfectly in my opinion, since it amplifies the hilarity of many of the circumstances. In episode 3 you're introduced to the triplets' father, who is drawn in a rough/sketchy style. I find it makes for a funny contrast between him and everyone else. The animation is fluid and consistent in terms of quality, with often exaggerated expressions for added comedic effect. This works seamlessly in my opinion.
As for the bg art, there isn't really much to say other than that it's drawn to compliment the simple character designs. The bg coloring is appealing with a muted palette, which sometimes exhibits a slightly marker rendered look.
Sound - This is where many shows fall flat in, typically not having anything praise worthy. The seiyuu's are noteworthy, especially Tomatsu Haruka (known for voicing Lala Deviluke from To LOVE-Ru) and Shimono Hiro (known for voicing Akihisa Yoshii from Baka To Test). The voice work is well done and brings out the characters' personalities really well. The sfx and atmospheric music also deserve to be praised, since they play an important role in the comedy. There are some truly hilarious sfx here and music that cues in at just the right time. The blood draining sound is especially amusing.
The OP also deserves mentioning for its cute and catchy tune.
Character - We have the 3 Marui sisters, Yabe-sensei (main teacher), Kuriyama-sensei (school nurse), as well as many side characters that are introduced in more detail through various points in the story. The triplets consist of Futaba who is the perverted muscle girl, Hitoha who is the dark and gloomy one, and Mitsuba who is the sadistic type as well as the self proclaimed king of the class. The inexperienced, newly transferred teacher and super clumsy school nurse round out the main characters. There is also the father of the Marui sisters, who looks like a big, creepy pervert. I'd also mention all the other secondary characters, but I'd need a lot more space to describe them all. Needless to say, they all have their own unique personalities that get their spotlight as the anime progresses. Overall, a great and entertaining assortment of characters make up Mitsudomoe.
Enjoyment - I'm loving this! Simple as that. Sometimes gag based shows are needed to change the pace and this manages to do just that for me. The relationship between the triplets and everyone around them is entertaining and I can't help but cheer up after watching each episode.
Overall - If you loved Azumanga Daioh, then you will probably like this. Keep in mind that even though Mitsudomoe has a very innocent air about it, it is meant for a more mature audience largely because of the adult humor. If you can appreciate humor the way I do, but at the same time are not easily turned off by the cute art style or the adult themes, then give Mitsudomoe a serious consideration. You won't regret it.
