Second of all; this may contain a few spoilers.
Big Order is the kind of show that throws in a bunch of interesting concepts, but ultimately barely does anything with them. --The ideas, the characters, the setting are all there just 'cuz. I'll tell you why further below;
STORY: 3/10
The story can be effectively summed up like this: ''Woah. Huh. Uhhhm... Eh...? Eeeehhhh... Ugh... UuuuUUuUUUGHHHH.''
Did you understand it? No? Yeah, me neither, because the story is all over the place --Due to being only 10 episodes long, from episode 2 onward, the story is rushed to ridiculous extents, giving almost no time for the viewer to process just what the hell is going on and leaving no space for proper world-building.
Around halfway through the whole thing you're more likely than not to drop the show because at this point it's evident than even the plot itself doesn't know where to go. This is due to the introduction of short subplots that contribute very little to the story because they were dropped so quickly. And yeah, these chunks of story are introduced as suddenly as they are thrown into the trash can. It's almost as if the writers forgot that they only had 10 episodes to wrap up the whole thing, when they had already taken their sweet time to build up the first half one of these ''side quests'', so they decided to rush the second half and get back onto the main plotline.
The show is full of all kinds of asspulls; for example (minor Spoilers ahead), there's this one time where Hoshimiya Eiji --our beloved protagonist, is being attacked while he's underwater by no less than an elder Aquaman-wannabe and his Order, Elementor. Thing is, he needs to counterattack before he runs out of air. His magnificent strategy? Control the fishes nearby and literally throw them at his attacker. And yes, it works. And yes, this anime is meant to be taken seriously, somehow. There are many, many more, but I'm too lazy to write all of them.
ART: 6/10
It's okay. The colors are somewhat generic but pleasant to the eye and the backgrounds have a fair amount of detail put into. It's got more or less the same art style and character design as Mirai Nikki but with more washed out colors. There are three things, however, that really put me off about this show's visuals;
FIRST: generally choppy animation.
I'd even go as far as saying that series like Dragon Ball and One Piece have a far more solid animation than Big Order's, and we're comparing long-running shounens with a /10-episode series/.
SECOND... sigh: CGI.
Alright, alright, not /all/ anime fail miserably at it, but the use of CGI on the industry of Japanese animation has gained the popularity of being a pretty hit-or-miss move. In Big Order's case, it's a lost swing. The models' movements are unnaturally stiff, and it doesn't help that the models themselves look like they were done in an hour or so.
THIRD... SIIIIIIGH: EXTREME censorship.
On the second episode, we get to see Kurenai Rin-- one of the main characters of the series, grope and then literally /squeeze/ Eiji's balls. On the fourth episode, we're introduced to Heavy Rockstar --the brown-skinned beauty on the cover of the show with huge, juicy tits bouncing around for your viewing pleasure. The following episode's where the problem really shines --Literally.
From this point on, expect huge, and I mean HUGE beams of light to cover a character's naked body. It's like the director said ''Gentlemen, at this point it's obvious that nobody's going to buy the Bluray version for shit unless we thrown in even more fanservice, but just to be sure, we'll cover /all/ of the skinny bits so that the thirsty members of our audience buy our garbage series! GENIE ASS!!!''
SOUND: 5/10
For the most part, pretty mediocre. I've got to say, though, I found myself repeating the opening theme for a while. The ending theme, while not nearly as memorable, has a nice tune and fits the atmosphere of the show.
Now, let's stop for a second. I want you to picture someone getting back-stabbed while ''I Love You, You Love Me'' is playing in the distance. That's more or less how 70% of Big Order's ''dramatic'' scenes play out. There's this one cheesy-as-fuck jazz track that, while kinda catchy, is guaranteed to turn any intended-to-be serious moment into a cheesy 90s action show scene.
CHARACTERS: 5/10
Do not expect much character development from nearly anyone here, nor any sort of redeemable backstory --out of all the 15+ characters the series has, only Eiji, Sena, Rin, Iyo and a few others, actually have some sort explanation to as of why are they doing what they're doing. Other than that, everyone else just seems to be there because the plot demands them to do so.
Note: Heavy Rockstar doesn't actually do much for plot progression, despite being in the show's poster. It's kind of like what happened with Sonic in Wreck-It-Ralph. She's probably just there so that you'd stare at her tits and consider watching the show.
One thing I'll give to both the show and the manga is that the character designs are actually pretty damn good. Not only that, but there actually was some potential for most of the characters to be pretty interesting and likeable, but the show once again played himself like a horny teenager and let out a hot, sticky load of wasted potential.
ENJOYMENT: 5/10
Pretty sure most of my enjoyment was because of how laughably bad this got at times. The subpar writing, lazy animation and poor sound choice all make it a true challenge to take the show seriously.
OVERALL: 4/10
I wholeheartedly recommend you to stay away from this anime. Even if you turn your brain off, I think there's other stuff out there more worth your time. Instead, I recommend you to check out Mirai Nikki if you haven't already. It's not a masterpiece by any means, mind you, but at least doesn't insult your intelligence nearly as much as Big Order does.
