I actually bought the DVDs. Don't make my mistake. I didn't mind it at first, but my opinion went downhill until I pretty much hated the show by the time I'd finished ep.12. I'll be avoiding Season 2 and I didn't even bother watching the mini-episodes I found in the disc extras.
It's a comedy about a Squid Girl, aka. Ika Musume. She's going to conquer the land! Cower in fear, puny humans! However she hasn't realised that there are quite a lot of us, or that the Earth's land mass is large. As villains go, she's pretty rubbish... but also fairly likeable. She herself appears to be a loud, overconfident ten-year-old girl, although she does have prehensile blue tentacle hair and the ability to vomit squid ink. She's lacking in social skills, self-awareness or knowledge of anything that's not in the sea. She ends up working as a waitress at a beach cafe.
She's also to blame for a tsunami of horrible squid puns. (In the English subtitles, they annoyed me for a while, although I've been told their cheesiness is more endearing in the dub. In Japanese, I wasn't so bothered.)
Theoretically this is a fairly standard light comedy anime. Amiable characters have fun together in episodes that tend to comprise two or three disconnected comedy segments. Silliness is had by all. There's a lively supporting cast, some of whom I liked, while I enjoyed ep.10. Nonetheless I still dislike the show as a whole, because:
(a) it's doing unfunny jokes that seem to have mistaken "implausible" for "comedy". These didn't make me laugh, but instead broke my suspension of disbelief.
(b) it's basically empty. It's slice-of-life silliness that just exists to amuse and is heavily dependent on the audience's fondness for the show and its characters. If you actively dislike one or both... uh, whoops.
(c) I want to kill those three American scientists who think Ika Musume's an alien. Partly it's their accents, although it also doesn't help that they're annoying twats with zero plausibility. (Of course it's possible that anyone who heard me would hate my accent in Japanese, but part of the problem is that I'm not hearing real Americans. They're Japanese voice actors pretending to be English-speakers, of course.)
EXAMPLES OF STUFF I DISLIKED (ep.11)
I can't ignore the American scientists and their antics, e.g. the invisibility suit, which for me was the episode's most annoying part. "We couldn't ignore the possibility that Chizuru is an alien." BUGGER RIGHT OFF.
That's not the episode's most insulting bit, though. Everyone goes mountaineering and Ika Musume doesn't see the point in going. (This is not a funny premise.) Halfway up, they meet an implausible succession of animals! Two squirrels appear, followed by a monkey, a bear and a cobra. (Does Japan have cobras? Google is my friend... no, they don't live there.) Ika Musume has a fight with the cobra, as you do... and it beats her up. It doesn't bite her and inject her with lethal poison. Instead I guess it just punched her or something. With, uh... its fists?
Later, Ika Musume reaches the top of a mountain and has an argument with herself because she doesn't understand echoes. Firstly, she's had them explained and demonstrated to her. Secondly, it's another example of this show's comedy beats being, as far as I could see, merely a demonstration of stupidity.
(I don't mind the episode's first segment, though, which is playing with Sinister Doll horror tropes.)
EXAMPLES OF STUFF I LIKED
Ep.10 is funny. (a) Ika Musume's artistic skills are a hoot, with her superhuman tentacles drawing how she sees people in her heart. (b) Sanae's lesbian traumas make for quite a compelling segment, with her delusions and hallucinations. She's trying to cure herself. (c) The third segment involves Ika Musume's ordinary human friend, Kiyomi, who improves the show with her presence. She grounds it. Here they're having a comedy baseball match, which I enjoyed although Tomoko had various criticisms. (The shattering bat appeared to be made of wood, but we also hear sound effects of metal bats. Metal vs. wooden bats would be an unfair match. Wouldn't junior high schoolgirls normally be playing softball, not baseball? Et cetera.)
I also don't mind the cast, mostly. Nagisa takes Ika Musume seriously as a would-be invader and is terrified of her, which is amusing. Kiyomi feels real, although she's hardly in it. Sanae has dramatic and comedic drive (i.e. she fancies Ika Musume).
I didn't mind the first few episodes. People were being idiots, but that's hardly unknown in either comedies or anime. After a while, though, I stopped being that interested. My notes for ep.8 are "I WAS HALF ASLEEP, I DIDN'T CARE". It involved umbrellas. That's about my level of involvement. The show's capable of being funny (e.g. Ika Musume going all-out and playing dirty at beach volleyball in ep.12), but it's also capable of treading water with material that's basically just dead air. It won't have a comedy premise. It'll just be something silly happening, with no attempt to put a twist or a slant on it. I wouldn't be laughing. I wouldn't be alongside the characters. I'd be trying to analyse the creators who decided to put these scenes in front of an audience. Admittedly my opinions clearly aren't universal since this show went on to get a second season and some OVAs, but even reviewers who like this show are capable of calling it "a series enjoyed most when you switch your brain off and relax". Personally though I'd rephrase that as "startlingly full of characters being stupid, even for a light comedy" and "best enjoyed by setting the discs on fire".