It's an interesting idea for a series. If they'd fleshed it out with more episodes and more clarity about the important things, it might even have become good. I watched it happily enough and it gave me things to think about, but it feels a bit chopped up and I can't imagine ever wanting to rewatch it.
It's the year 2072 and the world has had unlimited free energy since the discovery of Dimension W. That's the fourth dimension. Is it time? No, it's alternate universes. Or possibility. Or dreams, or memory. Or something. At first glance it's silly, but it's not unlike quantum mechanics if you start thinking about it. This is what the show's built around, obviously. It's fundamental. You can't give the world unlimited free energy and expect everything to remain the same. It's interesting and imaginative, but I think my problem with it was that the show didn't question it enough, or give enough focus to how weird it is. It's doing quantum things in the human-scale world. You could explore the hell out of that. If it's driven by dreams and memories, let's explore fairyland! If it's about parallel universes, let's... well, personally I'd stop watching the show. There's something not a million miles away from a time travel angle, with traumatic and vital backstory,
I found Dimension W more interesting than most of the characters and storylines, but it tends to get treated simply as technology. Scientists research it. Corporations sell it. (Theoretically it's free, but getting at that free energy involves building sixty giant towers around the world. New Tesla Energy has a monopoly and they'll have you arrested if you violate it. Unauthorised energy-generating "coils" are illegal.) I appreciate all this economics and worldbuilding, even if I don't think we ever learned exactly why New Tesla Energy used to go around killing its own research geniuses and so on.
(This anime is based on a manga and by all accounts it's a condensed adaptation. I'm sure the manga's better. Unfortunately I didn't like this anime enough to suggest reading it.)
The characters aren't very interesting, but partly because even the better ones don't get enough to do. The two you'll remember are the protagonists, Kyouma Mabuchi and Mira Yurizaki. Kyouma is an unpleasant ex-military thug who's rude to everyone, including Mira. He's the kind of person who can't be bothered to save your eyes by mentioning that he's just thrown a flash grenade at baddies. At first I disliked him. However he's been through the wars (literally) and he's both unwavering and loyal. In the end, he's actually sort of cool.
Mira is much more audience-friendly. She's a nice robot girl who works with Kyouma and has almost as much important backstory as he does. I was watching the show because of her, to be honest.
After that, there's... um. There's nothing wrong with the cast, but this isn't a character-focused storyline and so no one stands out as much as they should. Loser and his daughter are reasonably memorable, I suppose, but even they can slip out of focus when he doesn't get enough story time and his fight with Chrysler is resolved offscreen. Hang on, wait. He won? When? Oh, between episodes.
It's a watchable show. It's got some good SF ideas and lots of action, but it's the kind of show where you think "that would have been better with a few more episodes". You watch it and it's not that bad, but afterwards you'll delete it and never think about it again. The emotion and ideas are there, but they'd have come across more strongly if they hadn't been fighting against technobabble and a lack of story clarity. It definitely had potential, though.