Ass Pull: Just like the VN, Archer's appearance at Ryudou Temple in episode 24 is considered ridiculous by some fans. After running low on mana and being attacked by Gilgamesh, Archer shows up twelve hours later and saves Rin and Shirou from the Grail, with no one wondering how he's still alive.
For people who felt that the soundtrack was bland and forgettable , Episode 24 redeemed it in the eyes of some naysayers by bringing out a bunch of well-received remixes of classic tracks from the visual novel.
Shirou. Many of his same character traits from the visual novel are present, but many of his inner monologues and some of the complex logic behind his actions is removed, which can give anime-only viewers a different perception of him. This is especially evident between viewers who have read the visual novel (they understand him very well and are much more sympathetic to him) vs. new viewers who have been introduced to the Fate/Stay Night franchise through this anime (where he is borderline The Scrappy and The Load to these people).
Broken Base: The fact that in Episode 22, ufotable chose to use the Bleached Underpants version of the mana transfer scene from Realta Nua (complete with Narmy CG dolphins) rather than even hint at Shirou and Rin having sex pissed off a portion of the VN readers who were expecting the series to not shy away from some of the more mature material. Others prefer the Realta Nua scene, feeling that it makes more sense in the context of the story and Rin's characterization, and that the original sex scene was a Big-Lipped Alligator Moment.
"Unlimited Budget Works." due to the out-of-this-world animation, which, as of 2014, was arguably the best-looking anime that had been broadcast on TV at the time. Some would even go so far as to say it's the best-looking animated television show ever shown.
Kinoko Nasu's hard-to-translate writing style provoked a couple of hilarious subtitles that have joined the infamous People die if they are killed from the VN and the 2006 anime. Except that this time they don't have the excuse of being fan-translations.
People comparing the Lancers from here and Fate/Zero, especially after Cu Chulainn is forced to kill himself like Diarmund was. Cu Chulainn's line "I wouldn't be much of a Heroic Spirit if I died right away from a scratch like this." evokes images of Diarmund being pissed at the implicit insult.
Kougami Eliminated Shinjiexplanation Gilgamesh stuffing Illya's heart into Shinji caused him to swell as if he'd been shot by a Dominator in Eliminator Mode. It's made even better since Gilgamesh and Kougami share the same voice actor.
DOLPHIN explanation : Episode 22 has the 'mana transfer ritual' between Shirou and Rin, which featured CG dolphins in the DEEN movie adaptation and Realta Nua remake, so many fans have been crying out DOLPHIN in anticipation. They were proven right when ufotable did indeed use more CG dolphins in lieu of the sex scene. Well, mutant dolphins at least...
Kill Steal!explanation : In Episode 24, Archer kills Gilgamesh instead of Shirou. As a result, on reddit there are a lot of comments basically amounting to Archer 'kill stealing'.
Unlimited Salt Works◊ explanation : Due to some exaggerated reaction from fans who were very disappointed with the adaptation, people started to use that term when someone was ranting too much about the series (even in the things that ufotable adapted well).
Rin is a rhino explanation : Refers to the Off-Model way that noses are drawn throughout the show, ironically in an attempt to be more on-model with the way original character designer Takeuchi draws characters nowadays. Usually attributed to Rin because she appears first, plus the obvious name pun.
Archer definitely crossed the line when he left Rin completely helpless so that Shinji could rape her. This is more of a case of Adaptational Villainy, as Archer (despite everything) had every intention of protecting her in the VN, but was left with only 10% of his power after his fight against Saber, thus leaving him unable to make a proper stand against the clearly-antipathic Gilgamesh; this makes it understandable that he would have to make the decision to pursue his plan to kill Shirou over getting killled by Gilgamesh and leaving Rin unprotected either way. However, with the anime throwing that entire detail into question due to Archer still being able to materialize Unlimited Blade Works (a reliable counter to the Gate of Babylon) against Shirou, it really makes Archer's actions seem a lot colder by comparison.
Gilgamesh takes a flying leap over the horizon with his brutal beatdown and murder of Illya.
After Illya and Berserker's deaths Rin and Shirou sit down and have a chat about Gilgamesh and his epic. While in the VN this information is unnecessary since players would have already played through the Fate route and therefore know what Gil's deal is the anime needed to introduce him to its audience for this adaptation. Unfortunately, they decided to do it with a painfulexposition dump where they discuss his epic and status as the first hero. Now, while it's a little bit of a stretch that the two would know something as obscure as Gilgamesh's Epic off the top of their heads, it's not completely impossible. What's ridiculous is that the two then proceed to guess, with 100% accuracy, how exactly his Gate of Babylon works and why, which is such a bizarre leap in logic that it could only come about if the two had glanced at the script beforehand.
In Episode 21, Shinji being warped and mutated by Illya's heart into the grail core is indeed horrific... but then a bunch of disembodied arms come out of nowhere and turn it into a Big Ball of Violence reminiscent of something you'd see from a Looney Tunes episode, turning the scene from horror to pure hilarity. And even then, with a different character it might still have been frightening or disturbing... but in this case, it's Shinji, so it's 'k.
"Just because you're correct doesn't mean you're right" is pretty much the new "people die when they are killed" in that the intention is meaningful and works in context ("just because you're factually correct doesn't mean you're doing the right thing"), but the redundant-sounding wording turns it into hilarity.
One-Scene Wonder: Both Luviagelita Edelfelt and Waver Velvet (as Lord El Melloi II) appear in the last episode of the series during the segment of Rin and Shirou living their lives in the Clock Tower. The former has one of her classic rivalry scenes with Rin (with a short but well-animated fight scene), while the later has a brief but interesting conversation with Shirou about his ideals.
Rescued from the Scrappy Heap: Many fans generally agreed that despite what they thought Shirou initially, the events of Episode 20 completely redeemed his character.
Ship-to-Ship Combat: Comes with the territory of being an adaptation of a visual novel with several possible love interests.
Shirou/Rin is the Official Couple of this adaptation, and although this pairing has a big share of followers, there's a number of viewers who think Shirou has more chemistry with Saber (and to be fair, she already has a route of her own).
Then there are those who still thought Rin was a much better match with Archer (even after he betrayed her, kidnapped her and gave her to Shinji), although this one has been an FPC since as long as the original VN has existed. It's ironic because Archer and Shirou are the same person, so in the end Rin's going to end up with him either way.
Tainted by the Preview: While the recast was expected by most people, Shirou and Archer being recast for the English version did not sit well with English-speaking fans.
The anime started adding more and more original scenes while downplaying a lot of other elements from the VN (in particular internal monologues and explanations of some of the verse's more complex subjects). One major point of contention was the anime's expansion of Caster's backstory with her original Master, which Type-Moon vets felt took time away from other plot points that needed to be addressed.
The English dub cast was announced on July 2015, and... to say that Bryce Papenbrook as Shirou is controversial is a pretty big understatement. Replacing Liam O'Brien with Kaiji Tang for Archer also got people worked up (though this ended up working out, partially because it turns out Tang is an enormous fan of Fate and Archer and turned in a killer performance).
They Wasted a Perfectly Good Character: A somewhat... odd example in the case of Sakura. Although there are some nods to the events of Fate/Zero, her torture at the hands of the Matous isn't addressed in this anime because it wasn't meant to be outside of Heaven's Feel. The Heaven's Feeladaptation movies of course make this a core plot point, but coming right off of F/Z it can feel disjointed.
They Wasted a Perfectly Good Plot: Simply put, if you watched Fate/Zero before this and expected Unlimited Blade Works to be a direct follow-up that gives closure to all of the plot points from the prequel series, you would end up... disappointed. Sakura's torture by the Matous isn't even remotely brought up. Gilgamesh's Hidden Depths and subtle character development from the prequel where he showed himself capable of mercy and even camaraderie with his enemies is nowhere to be seen at all. Illya's past and potential to bond with Shirou as siblings who both shared Kiritsugu as a father is thrown under the bus as Illya gets brutally killed before she can make any real connection with Shirou. Rin does find out that Kotomine was the one who killed her father but by that point, she isn't in the position to take any revenge. The only thing that really carried over from Fate/Zero to this series is Waver, and his appearance is brief.
Tough Act to Follow: Among other issues, the main one stigma against this series is that it's a follow up to Fate/Zero's anime adaptation, which received near-universal acclaim. So naturally fans were a bit disappointed that this series doesn't build on what Zero established (beyond a handful of continuity nods) and the scale of the Fifth Grail War is much smaller than the Fourth, with a more constrained narrative.
Additionally, after Archer betrays Rin and Shirou to Caster he intercedes on their behalf. As Rin used to be his friend sparing her is somewhat understandable. What isn't however is him saving Shirou. Free from Rin's command spell all he has to do is ask Caster to let him kill Shirou personally and he wins. Instead he inexplicably lets the only person he wants to kill live and ultimately get stronger.