After a long philosophical chat, the Assassins turn up. Unlike everyone else there, they obviously means business. Rider offers them some wine, too.
During all of this there's also a part in which Gil claims that the Grail belongs to him because all the treasures of the world belong to him. Saber responds to this by saying that Caster isn't the only insane one participating in this war. The expression on Gil's face in reaction to this is priceless.
During a very serious conversation with Lancer, Saber and Waver, Iri´s cellphone rings, courtesy of Kiritsugu. Seeing her fumble with it for a good 5 seconds trying to make it work is hilarious, before she passes it on to Waver.
Rider's Running Gag of flicking Waver in the head hard enough to knock him down. Constantly. Half the time for no good reason other than "you're acting kinda stupid." Or "you're acting logical." Or "I feel like flicking you in the head."
Rider and Waver's interactions in general are usually hilarious. In the course of one episode, Rider drags a visibly terrified Waver to the top of a tall suspension bridge (with poor Waver crying to get down) and when he finally does get down, Rider charges straight into the middle of a battle loudly announcing his true name and intentions with Waver staring, flabbergasted, from the back of the chariot at what an idiot his servant is being....again. Following that, as the tension escalates with Lancer and Berserker vs Saber, Rider swiftly dispels that by...running Berserker over. Literally. With his chariot. With Waver giving a pathetic "how did I get into this mess" look as he's dragged along. This troper literally had to pause the video to stop laughing.
And to one up himself even more, the next episode has Rider essentially trading the head of one of his opponents, a Heroic Spirit called from beyond the reaches of time to battle in the Holy Grail war, for a pair of pants. A pair of mega-sized pants. Why? Since he doesn't want to lose to Saber who is allowed to wander around as long as she's wearing modern day clothes. Rider in general is hilarious.
In the third episode, Rider decides that Bill Clinton would be a formidable opponent.
A dazed Kirei, waking up to see a naked Gilgamesh grinning down at him, immediately asks if Gilgamesh has done something to him. Specifically, if Gilgamesh has healed him, but given their prior Ho Yay, you may wind up chuckling in the midst of a serious, tragic scene.
Speaking of Caster, let's step back for a moment and take a look at his obsession with Saber. A French veteran of the 100 years war, mistaking the most famous English folk hero ever, for Joan of Arc. The sheer Irony of that is so funny it hurts.
How about True Assassin being killed like an insect by Iris' giant spider construct in the Blu-Ray special episodes?
Gilgamesh's massive ego strikes again in Episode 24. Just look at how he proposes to Saber! Stabbing her in the leg with a sword, then telling her to give up her ideals and become his wife. When she (understandably) refuses, he states that he was not asking for her opinion, it's just what he decided.
Horrifying as the scene's implications are, Gilgamesh getting angry at Kiritsugu for "interrupt[ing] my wedding ceremony" was hilarious.
This Troper had to pause in the middle of the climax of the series and laugh for a good five minutes at the "wedding ceremony" line before continuing.
Saber Vs. Lancer, epic duel, just about to hit it's climax. Enter Rider who barges in on his Noble Phantasm and offers everyone to join him after announcing his name and class. Everyone's face is in some variation of Flat "What.". This includes Waver, who by all means, should be his master.
The Einzbern Consultation Room.
Caster being a huge fanboy of Jeanne. Having a freak out and then being poked in the eyes by Iri to calm down. To top it all, Jeanne used to do the same thing to him when they were companions.