My biggest problem with UBW is in how little you care about any of the characters.
Take Ilya for example. For the first half she gets portrayed as a sadistic, playful villain, but then disappears until her death scene. Then right before she dies they hastily show a huge chunk of her backstory, and expect me to actually care about her death? That's lazy writing as far as I'm concerned. Maybe they show more of her in the other route you are supposed to have read beforehand, but in this regard the anime totally fails.
Rin is perhaps my least favourite character of the entire series, boring and one-dimensional. I can hardly think of any character traits to describe her that isn't covered by "tsundere". And god damn talk about ridiculous actions, in one moment she tries to kill/seriously harm Shirou, and then she just decides not to. And suddenly they're working together!
This is also one of my biggest problems: plot-conviniences. The most infuriating thing about UBW is how they are actively fighting a war, where everyone has certain ambitions and wants to win the grail. Yet, whenever someone has a chance to kill someone, they don't. Why? "I just don't feel like it" or "I can do it later". LOL! This also ruins several fight, since you know none of the characters are in any danger, and therefore it lacks tension. And why the hell do all of the masters come from the same fucking school, all of this seems so overly convenient and stupid, but maybe it's explained in a different route?
The only characters that are slightly interesting are Shirou and Archer, but the way they beat your head over with their ideals and how heavy-handed the themes are makes it pretty awkward. A bit of subtlety would have done a lot of good. The side-characters are either completely wasted without any development (Saber, Kirei, Sakura (not her route, I know)), or generic, borderline cartoonish villains (Caster, Shinji).
I also have some more minor gripes with the show, especially the slow pacing, slice of life moments and how they spent an entire episode for the cringy mana-transfer. I'm not saying that Fate/Zero is a masterpiece either, but at least it was a hell of a lot better than UBW as a stand-alone anime. Maybe it'll change when we get HF and if I ever decide to pick up the VN again, but so far I'm not very impressed.