The battles and form-changing have been treated with respect and care to the plot, to the point where even if the start of the fight, or the outcome of the fight doesn't have any real meaning, something happens during it to lead Shotaro and Phillip toward the conclusion of the case.
The characters for the most part are pretty well rounded and human. The Fuuto Irregulars and Akiko were pretty ugh inducing at the beginning of the series, but they've mercifully have been toned down and still do fit with-in the overall scope of Double as Shotaro's trust-worthy word on the street. These past fews arcs have also done really well for Humanizing the Villians and Wakana (I really can't bring me to call her a villian anymore.), making them both ruthless wall to over come, while still prone to human error. Acting wise, it's been pretty passable, with Shotaro being the best of the bunch. Though pretty much everyone has been improving as they have settled into there roles.
The BGM's and music
Best thing I have to give Double is the amazing consistancy the writing/tone of the show has had. Outside of the Heaven's Tornado arc (easily the worst arc Double has thrown out.), the show has been pretty damn good at keeping it's tone consistant and well, moving the plot forward. Both sides of the struggle have gained information on the other side as things have progressed, with both sides not quite having enough information/power to make an all out attack on the other. It's not the fasting moving Rider plot, but it's not insulting out intellgence making us wait till the end of the year to really do anything, expect pimp out more toys.
Accel's introduction could change a lot of this, the show still has a lot of episodes to go. But as of now, I'm really impressed, and give this about a 9 out of 10 if I must give it rating. This is definitely a series you don't want to miss! :)