I'm undecided as to whether or not the final two episodes of GIRLS und PANZER qualify as part of the winter 2013 season. They were delayed from the autumn 2012 season and should probably belong there with the rest of the series, but then again they did actually air late in winter 2013. There are only 40-some minutes of new material, but that's more than Teekyuu, so it arguably has as much right to be here as the various two-minute shows. Whatever the case, these two final episodes of GIRLS und PANZER were far and away superior to any of the other shows from winter 2013.
Vividred Operation managed to both be low-brow and ambitious at the same time. From a conceptual standpoint, it is a silly bit of science fiction (arguably fantasy) with a lot of narrative problems and plot holes that cannot survive even casual scrutiny. On the other hand, it was lovingly produced at a high standard by people who obviously wanted to make Vividred Operation the best show about anime butts they possibly could. None of it ever made any sense, and the show really suffered towards the end when caring about the character drama kinda required it to make at least a little sense, but overall it was still a good series. I can't fault a show that is otherwise so well executed, even though measured expectations are a critical part enjoying the show.
If anything, JoJo's Bizarre Adventure requires even greater suspension of disbelief than Vividred Operation. Nevertheless, I think most JoJo's fans will give the show a pass because it is "awesome" or "cool" whereas Vividred Operation is "embarrassing" or "stupid." Why is that? Because fansubbers helpfully included the mid-broadcast commercials for action figures and video game tie-ins, it is apparent the core audience is just as likely to be small boys as it is older fans who have actually read the 63-volume manga which ran from 1986 to 1999. What gives JoJo's Bizarre Adventure credibility that its fans seem unable to extend to fellow Weekly Shounen Jump title Medaka Box (for example)? Is it because the former is about beefy fabulous men flexing and posing for each other in totally not-gay ways while the latter features (ugh) girls and their (UGH) breasts? I think it's probably something as simple as the target audiences merely having different tastes and expectations in conjunction with a pompous sense of superiority fans of beefy-men-anime feel over fans of cancerous-moé anime. The message seems to be that it is appropriate for adult men to enjoy cartoons intended for grammar school boys, but it is inappropriate for adult men to enjoy cartoons intended for junior high school boys.
So anyway, JoJo's Bizarre Adventure is entertaining and silly and packed wall-to-wall with exposition as characters incredulously describe increasingly implausible events that unfold through contests of one-upmanship and tensionless fights. It's fun to watch, and historically significant within the shounen manga canon, but don't fool yourself into thinking you're a better anime fan for liking it compared to some guy who maybe prefers to watch something else, even if that something else is about autistic girls eating cake and making vaguely catlike noises. Who knows, maybe there's someone out there who enjoys both.
I had fairly low expectations for Oreshura and had predicted that it would be doomed to a non-ending anime ending because the source material is still ongoing. Surprisingly, after a dull middle portion following the Chiwa-bullying beginning, Oreshura managed a succession of great moments and a few really good episodes to finish out its 13-episode run on a strong note. It even managed to work in a satisfying ending of sorts. It probably would have been best to end on the final episode's high note, but even the post-climax resolutions revisiting the remaining three girls weren't too bad.
I'm especially pleased Oreshura managed to turn Ai into a sympathetic character, although she laid on the postmodern1 tsundere aspect a bit thick. I don't think her character would have worked if viewers couldn't feel at least a little bad for her. The ending is open enough to permit a second season (with actual hope a second season wouldn't merely be a retread of the first), but conclusive enough to believe there was real conviction in Eita's decision and announcement in episode 13. From a harem comedy anime perspective, this is basically the best case scenario.
Even after 26 episodes, I still have no idea how to explain AKB0048. I think people may be right when they joke it's the Macross anime Kawamori always wanted to make. In all honestly, I have to believe there's a good chance AKB0048 may be what you get when Kawamori goes off the rails. I don't expect to ever re-watch the series because I never got invested in the characters (or their real-life AKB48 counterparts), but some of them are good company during the ride to see sci-fi battles with the power of song.
I don't think I would have liked Puchimas! -Petit Idolm@ster- nearly as much had there not been so much of it. However, enjoying most of the episodes will probably require prior knowledge of the basic iDOLM@STER canon. Since the episodes are so short, nearly all the characters are winnowed into exaggerated stereotypes of their simplest characteristics. (E.g., Chihaya is self-conscious of her small bust, Hibiki likes animals, etc.) When it clicks, though, it's quite entertaining and provides basic satisfaction quickly. It's anime junk food, in a way.
Dokidoki! Precure can be pretty good at times and boasts a solid lineup of competent Cures. However, the last two episodes from winter 2013 introduced the now compulsory magic baby character, killing all the momentum the show had. Hopefully this useless infant will either be marginalized for most of the year, or be limited to occasional happy burps like Chiffon was during the Fresh Pretty Cure run, because Dokidoki! Precure is much better off without this creature's antics. Now that I think about it, this is true of real life babies as well.
Smile Precure! had a reasonably solid conclusion, but it didn't have as much of an impact on me as it appears to have had on other viewers simply because I am not particularly enamored of Smile Precure!
Teekyuu is silly, but short, so although it had good moments it was difficult to get invested in this series. It's okay, but I gotta wonder if all the people who were really nuts for it were high.
Finally, Straight Title Robot Anime is another amusing short comedy. It's not as frenetic as Teekyuu and it has less diversity than Puchimas, but there is good chemistry among the three main (three only) characters. Fujii in particular is pretty charming. Unfortunately, it didn't take long before I lost interest in every segment except the improvisation portions which thankfully remain pretty good.
You can read about the shows I didn't finish here.