When someone on the Internet describes a work of fiction as 'visionary', it's usually meant as a form of praise, referring to a willingness to defy convention in favor of something more thought-provoking and enticing. As defined by a dictionary, 'visionary' refers to embracing fanciful and often impractical ideas.
Mawaru Penguindrum falls under both definitions.
What Kunihiko Ikuhara of Utena-fame has created here is a show that takes philosophical musings on themes such as fate, love and death; and combines them with slapstick antics involving ghost penguins and ping-pong balls that erase people's memories.
If that sounds difficult to take seriously to you, don't bother watching this show. It's going to get a lot weirder.
The overall product is audacious, if nothing else; presenting the story 2 brothers, Kanba and Shoma, who promise to help a mysterious entity track down an object called the Penguindrum in a desperate attempt to ward off the death of their sister, Himari. Their quest has them run into a slew of messed up characters and situations, and before long the narrative turns into a complete mess.
There are several reasons for this.
A big problem is that the series has absolutely no regard for logic and consistency, even within its own narrative. At the start of the series, Himari is brought back to life after succumbing to an incurable disease. Her death and subsequent revival are treated as tragic and miraculous, respectively. Makes sense. What doesn't is that this is repeated several times over the course of the series, treated with the same impact every time. Viewers, however, might be puzzled or annoyed by this repetition seeing as it raises the question as to how severely this series treats the concept of death. This is exacerbated once another character reveals that he's been dead for over a decade, after which the story moves on, completely unaffected by the revelation.
Character development also tends to be very inconsistent. Motivations, personalities and even backstories can change from one scene to the next just to suit the needs of the plot. The aforementioned memory-erasing ping-pong balls are liberally used to retool previously established plot-points to the narrative's convenience.
Other, basic issues also plague the storytelling: many of the back stories feel interchangeable (crappy childhoods galore), some characters who get a lot of screen time end up being completely insignificant while others are introduced seeming important only to be forgotten about before anything could even be done with them. The latter goings-on of the story also feature hackneyed developments involving terrorism, delusions (it's all in your head!) and cliffhangers (someone was stabbed! but who?) that end up not mattering in the slightest.
Most damning of all, however, is the clumsy way the overall product comes together. The shifts in tone – from whacky to dark and vice versa – are as frequent as they are jarring, and it all too often feels that the subjects about which characters are philosophizing have very little to do with the story of two brothers who are attempting to ward off that which should be inevitable.
*WARNING! The following paragraph contains spoilers about the general tone of the ending! WARNING*
Speaking of which, the ending cops out on that in a major way. The series spends a lot of time emphasizing how ordinary people are powerless in the face of fate and that struggling against the inevitable will often result in greater tragedy. One would expect such a story to end on a tragic note as is befit for a something that fancies itself an exploration of fate, but the actual ending turns out rather bittersweet; mostly leaning towards the sweet considering the dark events preceding it.
All that said, the series must certainly be praised yet again for its unique style. This show isn't just different for the hell of it. Ikuhara combines audio and imagery in striking ways, constantly delivering scenes that will shock and surprise. Even if you end up disliking the series, there's a definite guarantee that you'll remember it. Which is more than can be said for a lot of other stuff.
In closing, I'd like to say that while many others would opine that the Mawaru Penguindrum's unique style, impeccable direction and interesting themes make for a wonderful anime, I think that there are too many issues with the overall product to really consider it great. Many of which, I feel, can't be chalked up to mere artistic idiosyncrasy.