These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Carnival Phantasm
Ascended Meme: Fans often joked that the major difference between Saber and Saber Alter was that the latter didn't have her Ahoge and that she could probably will the transformation just by pulling it off. Cue Saber doing just that in Episode 8.
Another, more minor one is the idea of Archer having an Unlimited Food Works attack given his younger self loved to cook. In the Ilya Castle special, he assaults his enemies with a hail of cooking utensils.
Cargo Ship: Apparently, Assassin has developed strong feelings for the gate of the temple he's been charged with guarding. Cargo Bodyguard Crush?
A lesser example in the same episode is how quickly Rider takes to her granny bike, even giving it a name within seconds while blushing the entire time. Quite possibly also a Continuity Nod to Hollow Ataraxia where she offers Shirou anything in exchange for borrowing his bike.
Crosses the Line Twice: Sakura getting beaten up by Shinji in episode 6? Not funny. Sakura being sent to shovel the snow off the roof without any extra layers of clothing while Shinji stays in a warm house? Not funny. Sakura falling off the roof? Funny!
It gets even funnier when she leaves a Sakura-shaped hole in the snow, followed by Shinji opening the window to rapid-fire berate her, ending with an offhand demand that she go get the latest Shounen Jump magazine.
Informed Wrongness: In the date scenario where Shiki and Shirou chose Arc and Saber over dating all the girls, they get berated by them for not saying much sooner how they felt on wanting to make all of them happy and choosing the main heroines over them. And this comes after the other girls started to go all Yandere on them for not being chosen in the first place.
Magnificent Bastard: Caster, surprisingly. She's one of the few characters to get everything she wanted, and came close to winning episode 9's car race to win the Holy Grail without even bothering to compete in person. It took BerSer-Car screwing up Assassin to cause her plan to fail, but it's likely she wouldn't really care anyway that it did.
Sakura kicking Rider around just to make her point.
Rider gets Shinji to feel this way by doing a sadistic version of this that keeps getting him hurt every time he tries to be a Jerkass, basically an animated version of a doujinshi with the same plot. Bonus points for milking his perception of how useless she is and weaponizing it.
That whole segment, courtesy of Akiha's mind reverting back to being four years old. Lampshaded by Kohaku.
What Could Have Been: Sadly, there wasn't ever a combined session of Tiger Dojo with Teach Me, Ciel-sensei.
Sella and Kohaku at a table with Leysritt and Hisui; Taiga, Gilgamesh and Iskander at a table; Kiritsugu, Irisviel and Ilya at a table; we want season four!
The Woobie: Lancer gets abused in this OVA, so much so that people might actually start feeling bad for the guy, since most of the time he is just minding his own business.
Shirou and Shiki become this in the second half of the Hibi-Chika Special, especially with all the torment their love interests have put them through.
Saber has several moments: Not getting to nap with Shirou, getting curb stomped by Berserker, putting up with Gilgamesh in episode 8, having all of her hopes about the Holy Grail War being an honorable battle between knights being shattered, being denied food from not getting 1st place in the Ilya Castle Special stages, and having to potentially live on just tea and rice after Shirou spends all his money!