Due to various circumstances, I watched this on a TV and took no notes. So, here's what I can remember from this modern fairy tale (if I may borrow the formula from Tappan).
When I lampooned the summary of Ginban Kaleidoscope at ANN, I had no idea that I would watch it, let alone like it. But when Evirus called it "surprisingly good", he was right. Despite the premise, it is an unpretentious anime, employing competent storytelling, acted out by tolerable characters. The only part where I felt that something was missing was the final arc. It was underfilled like the final episode of Banner of The Stars: so many important events happened, the characters travelled and engaged into a high-stakes contest, but everything not directly related to the story was trimmed away mercilessly. Not that doing so damaged anything in the story, but the pace changed noticeably. Perhaps that is what made Evirus to wish for more episodes. I certainly would not like any more episodes tacked at the end.
After the finish, I researched Shizuka Arakawa a little bit. The anime was broadcast before the Olympics, and her outstanding gold was still in the fiture. So, it is unclear to me if Tazusa was supposed to represent her, e.g. if Miss Arakawa was a star enough to prompt a manga and a quick adaptation to TV anime. Yulia Lipitskaya was not a household name in Russia before Sochi.
One persistent schtick of this anime is that Tazusa (almost) always finds it necessary to reply to Pete's voice in her head, which typically leads to confusion and aggravation in those nearby. She can stop it if she focuses, like in a press-conference, but usually she mouths off before she has a chance to fight the urge. It was irritating, just not irritating enough to ruin everything.
The instruments in Pete's airplane showing nonsense were not irritating either. Disbelief, suspense!
Liked: Yes
Rewatch: Possible
P.S. Another anime with a ridiculous premise that was pretty good is Midori no Hibi (even has a category at Ani-nouto). Ginban Kaleidoscope, however, is more focused on the story and thus superior, IMHO. It fits da feels better, too.