I actually don't have a whole lot to add except to say that it was great the whole way through. It's part supernatural, part slice-of-life, part quirky comedy and part coming of age. It's never quite as good as Ame to Yume, and if you watch ATY before TTA, it becomes more and more obvious as the series progresses that it came about because of the success of ATY, but it was still excellent. The only time you really needed to know anything about ATY was when Sawamura Ikki(father) and Hayami Mokomichi(boyfriend) guest star...both ask Teruyo if they've met before and questioningly call her Ame, but beyond that, both of their appearances are just normal craziness for Sasara(this is a town where people thing a good way to have their granddaughter make a new friend is to hire another girl her age to spy on her)
Even though neither is a "Top 10" dorama for me(but I loved both to bits) Teru Teru Ashita and Kekkon Dekinai Otoko reminded me of why jdramas really are my favorite...even when dealing with the supernatural or pure crack or improbably events, there's usually a feeling of reality and humanity to the series that makes them stand out more to me...I mean, Gokusen wrung more emotion out of me than any modern kdrama or tdrama has, because the problems the characters face feel more real.
PS:
This is wandering around with an unrequited crush the whole series. Yes that does say "actor and host" in his bio. Yes, presumably it means that kind of host...I'm sure he does very well.