reasons I like the show:
(1) high production values. Same reason I liked X TV ... the plot there was just plain stupid (wtf dragons and seals ... bullshit pseudobiblical mystical babble ... two Kamuis ...), but the show is just so dang well put-together.
(2) good action... the fighting sequences are pretty impressive .... related to 1, more than anything.
(3) I like the characters. I like Shiro's hesitant naivete and self-sacrificing personality. I like the layers of Rin's personality ... the fact that despite talking big, she was able to put herself on the line to protect a friend (albeit a friend on uneasy terms). I like how Ilya's not just a one-dimensional villain, but rather is presented as a child given a grisly task to do and never really given a proper sense of right and wrong.
(4) The whole servants/identities thing is an interesting diversion. It's pretty meaningless, I'll grant you, but fuck man, what isn't meaningless about any given anime?
(5) Character growth. Shiro grows into his role (even while redefining it). Rin gets a chance to grow some humanity -- something largely denied to her by her upbringing as a magician. After Berserker goes down, you could see the potential for Ilya to become something of a decent human, too.
(6) Underdog syndrome. I, like most people, like cheering for the nice-guy underdog ... especially when you just sort of know the underdog has the potential to kick everyone's ass. While the people around him know what's up, Shiro's basically just dropped into the middle of a war with no skills and no knowledge of what's going on.
In short, I think this show essentially captures the good points you can have in any apocalyptic-type series. Sure, the plot is a bit shallow and light, sure the characters aren't exactly role models... but you know what? Any series set during a big potentially world-changing event is going to have that sort of flaw. Did you like Eva, despite shinji being a weak, spinless and revolting character and everyone else being horribly twisted? Did you like Rahxephon, despite the very very strange character development and the near-indecipherable mysticism? Did you like X, despite the fact that other than production values and novelty it had virtually nothing going for it? If you said "no" to all three, then why are you even bothering with this show?
I think you're putting too much emphasis on the "what's the servant's identity" minigame though. It's NOT essential to the plot to know that Berserker is Hercules, or Rider was Medusa, or Saber is Arthur. It IS essential to know that Rider is a twisted creature, matching the twisted personality of her master, that Berserker is an amoral beast that's really freaking hard to kill. Saying "well, this character has its roots in mythology" is one thing ... but they're really not dwelling on that so much, beyond using pre-existing tools to tell a new story.
Don't get me wrong, I can certainly see how you could dislike the show. Just ... the criteria you're criticizing it for are the sort of things you could blast just about any show being made today for -- lack of plot progression (amg anyone?), characters that you might not like, minor details that don't appeal to you. If you are seriously going to criticize the show, criticize it for its horrible non-combat pacing, or because you just don't like the characters, but I don't think it's fair to call minor points major ones or to omit the other good things about the series entirely because you're so hung up on those things.