It was the big surprise hit of the season, but don't let that lull you into false assumptions. It's light and amusing. It doesn't really matter very much. It's based on a manga by Cool-Kyou Shinsha (I Can't Understand What My Husband is Saying, Komori-san Can't Decline!) and it's about lots of supernatural girls who come to live with Kobayashi. They're not used to the human world, they're capable of destroying stuff if they're not careful (e.g. tower blocks) and they're cute.
Yes, even Fafnir. He's cute in a hostile cold tsundere sort of way.
What really lifts the show, I think, is Kobayashi's gender. There are lots of shows like this where the Kobayashi-figure is male and they're a lot harder to recommend to people. Even if the sexual fantasy angle isn't important at all (as it isn't here), you're still aware that this is a show where a huge-breasted fantasy girl glomps on to the main character, declares undying love and moves in with them. You'd be having to do a lot of explanations if you wanted to show it to your grandmother. This show, though, side-steps all that. Kobayashi's female, so she just doesn't care when Tooru's trying to get inside Kobayashi's knickers. She ignores it. Instead she judges Tooru on what she's like as a person and how much trouble she's going to cause... which is, to be honest, what's really important. There are some non-genderflipped shows like this that I really like, but the genderflipping just lets you forget about all those potential distractions and lets you focus on the comedy and the relationships.
The dragon stuff is cool. These really are proper fire-breathing dragons, so huge that they could crush cars without noticing and blow away inconvenient weather... but they can also do magic. In the human world, they turn into humans. They're a bit reluctant to do so, being basically evil and liable to sing happy songs about destroying the world and exterminating all life. (There's one good dragon and she's a bit hopeless.) They're not even consistent about their disguises, with Tooru usually sporting horns and/or a tail as thick as her torso. However their magic comes in particularly handy when they've just melted Kobayashi's apartment into a bubbling pool of lava and she might be upset if she came home to find it like that.
The show has two sources of comedy. The first is everyone's dragon side. Tooru's evil. She's hopelessly in love with Kobayashi and determined to be the best maid and housewife in the world, but she needs watching sometimes. Her idea of playing in the park is liable to turn the neighbourhood into a smoking crater. Dragon dodgeball is quite something. She also has a weird fixation on getting Kobayashi to eat her tail, which is literal rather than innuendo (the meat grows back) but I'm sure must surely have some not-so-hidden significance that Tooru never tells us about. Kobayashi's not interested.
The other, though, is just spending time with these people as people. Kobayashi, Tooru and Kanna form a metaphorical family (husband, wife, daughter) and you'll have episodes where Kobayashi discovers, for instance, how expensive it is to buy everything your child needs to start school. Kanna makes friends at school. Fafnir discovers the magical art of living with humans and even sort of becomes happy, although you'd need scientific instruments to be able to tell the difference with him. (He's got an attitude problem.) Kanna's school sports day coincides with Kobayashi's company work delivery date. Tooru goes out in town, makes friends with the local shopkeepers and mostly doesn't worry about her status as a particularly unusual type of foreigner. The gang put on a stage play for the local old folk, although they, uh, make some changes. (It started out as The Little Match Girl, but that's not where it ended up.)
There's some mildly dubious material with the younger characters. A school friend of Kanna's develops a massive lesbian crush on her, even though they're both at primary school. Shouta (same age) is a boy who's much too flustered by Quetzalcoatl's massive boobs and minimal clothing. None of this ever goes anywhere at all, but it's still dodgy and it's something you'll have to live with if you're going to watch this show. (Apparently it's a bit milder in the anime than in the original manga, though.)
This is a lovely show, but I think it would be misleading to call it a must-watch. Don't expect the Greatest Thing Ever. It's just a happy, funny show about silly people living together, being nice and bouncing off each other. No one gets killed or eaten (although luck plays a significant part in that). The series resolution with Tooru's dad is cool, although I was surprised that Kobayashi never considered going to the dragon world herself. (Maybe she was respecting Tooru's decisions?) I've just looked on Amazon and apparently there are seven animated mini-episodes on the Blu-ray releases. I might go looking for those too...