That was quite good. Its biggest problem, really, is that no one's going to watch a minor J-horror film called Teketeke 2 without having seen the first one... but that was a much weaker film, so it's a bad advertisement. Everything here's better. I'd give the sequel a modest recommendation, if you don't set your expectations too high.
It starts with a five-minute recap of the first film, which is leading somewhere brutal. Otherwise, though, this film's first half-hour is Teketeke-free. It's about nasty, scary schoolgirls. Reiko is a somewhat miserable-looking girl with a stubborn streak and a disinclination to let the class's alpha bitch (Tone) get away with everything. Natsuki is her only friend, who gets caught in the middle. Classroom politics, eurgh. We see in surgical detail exactly how Tone and her clique dissect Reiko's life, prise her friends away from her, steal her money and generally act like hateful scumbags who need bloodily killing.
Well, guess what. Teketeke's waiting offstage. (Note, also, that when one of the clique is found dead and bisected, Tone's only reaction is annoyance at having fewer lackeys at her karaoke session.)
The acting's fine. I believed in the people and the situation.
The backstory and mythos are significantly deepened. What we learned in the first film was only half-true, i.e. was full of lies. I struggled to buy the stuff about Teketeke killing you because of the kanji in your name, but then again the film never finally confirms the truth of this. On the contrary, it discusses the nature of urban legends and the possibility that the Teketeke we see here might just be one manifestation of that. There might have been a wartime one, for instance, whereas this film's Kashima Reiko met her fate in 1948. I liked all that. It fits the fairy tale quality of the "kashima" chant to get rid of her, for instance (and even that doesn't work as described).
Also, I never laughed at the sight of Teketeke herself. She doesn't bounce around comedically in this one and you get less warning before she shows up and kills you. She also inflicts a cool (i.e. gross) killing by mop.
This film has a point. It has a character-based story, into which Teketeke fits, whereas the original didn't have much in its head beyond "let's make some J-horror". It's also quite nasty and has a good ending. Had Kouji Shiraishi made a third Teketeke film, I'd have definitely watched it.