This is a good watch. After the first couple of episodes, I was definetely hooked up and I ended up watching it all in one go. It's a 12 episode anime, so there is basically no filler and the pacing is good. But, on the other hand character development is a bit lacking.
A couple of decades in the future, the world's energy problems have been solved. A new dimension has been discovered, dimension W, and scientists have been able to capture and harness the energy from this dimension using coils, devices that function similarly to batteries. Obviously, reality isn't this straightforward nor is it so idyllic: there are many things that New Tesla, the company that has patented the coils and that has monopoly on the production of energy isn't saying; while researching dimension W and the coils several tragedies have occurred and have been covered up, and the full potential of this new technology is still yet to be explored and understood. I really liked the opening scene where you see our protagonist, Mabuchi Kyoma, a tough no-nonesense-don't mess with me guy working as a mechanic in an outdated and anachronistic garage, surrounded by rusty car frames, while on the news they're saying that in 3 years time electrical cars will have completely replaced prior models and that gasoline prices have skyrocketed. He's a collector, a guy whose job is to collect illegal coils - but pretty early on in the story we find out that he hates coils and anything related to them, sticking to the old way of life with his gasoline-fueled cars and no-coils policy. While on a job he crosses paths with a female robot, Mira, who subsequently becomes his partner. I won't add anything else about the story to avoid spoilers, but Kyoma and Mira pair up to solve the mystery linking Kyoma's past to Mira's creator, New Tesla and the coils. The pacing is fast, the story keeps you on edge and the ending is quite satisfactory.
As for the characters, starting from Kyoma they're all likeable. It's only 12 episodes long, so most of the characters aren't given much analysis, depth or development. Kyoma is naturally the one with most screen time, he has a back-story that motivates him and makes his feelings, actions and reactions perfectly understandable. He doesn't exactly develop as a character, it would be more correct to say that he undergoes a sort of loop whereby at the end he regains an awareness that he already had and had lost. Mira is also a likeable character, even if she remains sort of a mystery to the end. For a robot, her feelings and reactions seem to be a bit too similar to a human's ones; but there are only hints about her nature. I don't know exactly why, but Miyabi reminded me a lot of Mayuri in Stein's Gate - maybe the relationship between Kyoma and Miyabi is very similar to the one between Okabe and Mayuri; it doesn't really matter. It's a plot-driven anime, so most of the characters have a precise role in the story to carry out and do just that. They aren't rounded nor detailed very much as characters per se.
Visuals, animation and sound are all pretty good.
Overall, Dimension W is an enjoyable anime. It's not great, it doesn't analyse its characters in depth nor all the implications of the world it is set in. But it's fun to watch and the story is engaging. So, thumbs up.