Most characters feel like they were rather well designed with only a few exceptions IMO.
Zod was disappointing since although I think his moveset is awesome and the character design is great, the moveset doesn't really fit the character. That moveset could have been adapted to fit a dozen of other DC characters and make more sense.
That said, if they'd tried to make Zod more like his comic/movie adaptations then we would probably have a much more bland character as a result, so I can't really hate on what they did with him too much.
That said, I do think Aquaman is pretty bland. I don't really know what they could have added to make him a better character, but I have to admit that other than his super, nothing really screams "King of Atlantis" to me.
Killer Frost is also bland to me, but I don't know enough about her as a character to give any input on how she should have been done. She just feels extremely generic to me. She's another character whose moveset you could just give to a dozen other characters and have it make more sense.
Also Joker is weird to judge. I like his concept and design, but as Qwark pointed out it wasn't really well executed.
That said, having his trait be a counter is kind of lame and doesn't really fit his moveset. I personally would have preferred a "bold cancel"-style command jump that worked based on charges that come back on a timer (Like Batman's trait).
I actually like Shazam's design though. I would have preferred a more creative trait, but then again I really don't know what else he could have gotten instead.
I also think Flash had a pretty good design. He does feel like the fastest man alive; able to cross the screen to punish in an instant or deliver enough hits to break armor. His dashes are also ridiculously good, as they should be.
While I like Martian's design (Minus the orb, which doesn't really fit the character), I wish they'd done something with his ability to morph his body. I know in the Justice League Cartoon there were a few episodes where he turned into alien species to fight and I was kind of hoping to see some of that.
That said, the Martian design we got was really cool as well.
Batman has a really really cool design though. He feels like Batman. The only thing I dislike about him is his blatant disregard to the laws of physics. There are a lot of characters in this game for whom a double jump could be excusable, but Batman is not one of them.
I do have to ask though: What the hell was their goal with Cyborg? I may be wrong as I have an outsider's perspective, but he seems like a zoner with missiles for setups, grapple for mobility and positive frame data more or less everywhere for general purposes, and yet nothing in his moveset seems to work in tandem. It almost feels as if they designed the fireballs and missiles, then took a break to do other characters, then realized before the game shipped they forgot to give Cyborg a real moveset and just slapped whatever they could think of onto him. For example, why does this character have a command grab (And why does it suck so hard)? Ugh... this character is just a huge disappointment.
That said, I do think Lex Luthor may have the best design in the game. I am constantly impressed as how they managed to turn him into a fighting game character when really he's a rich businessman, politician and criminal mastermind, none of which are really "fighting" skills, and yet his brilliant mind and unlimited funds, as well as the clumsiness of controlling an artificial robot body, are all present in his moveset.
Also GL... For a character who's powers rely on willpower and imagination, his moveset is surprisingly unimaginative. They could have kept all of his moves' properties and put construct animations on them and I would have been okay with that. However as it is now he really doesn't play the way you would think a Green Lantern would fight.
Bane's design is really cool too, even if the execution made him ridiculous.
Anyway I have spent way more time than I should have on something like this, so I'm done.