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While at the Plants Athrun is assigned two bodyguards. Why is it funny? They are Yzak and Dearka. Yzak is especially hilarious as he acts incredibly pissed, meanwhile Dearka stays pretty cool. This one line is the crowning jewel though.
Dearka: "So where do you want to go?"
Yzak: "And if you say shopping I'm gonna kill you!"
Shinn didn't listen during the briefing and finds out as he's flying through a cave that there is no light, and that he will have to rely on his radar to guide him. Reflecting on Athrun's assurance that he was the man for the job, he shouts:
"That bastard. He just didn't want to do it himself."
By itself, not funny. When you know that Athrun a) would totally do it himself, and b) that he thought Shinn was aware of the whole "no lighting" thing it becomes hysterical.
Kira nonchalantly flying the Freedom Gundam into the middle of a wedding to rescue Cagalli from her arranged marriage. Hysterical enough, even without Cagalli angrily berating him afterward for unnecessary dramatics.
Kira: "Wow, that's a pretty amazing dress!"
Cagalli: "Shut it!"
The scene is funnier when if you remember the similar scene in the previous series.
When Kira disarms the Astrays stationed as the wedding's security: after the first three have have had their rifles destroyed the last Astray tosses his rifle away so the Freedom won't shoot at him.
Lacus appearing as herself in the middle of a ZAFT base giving autographs, followed by being found out, Kira wrecking every mobile suit in the base and Meer arriving angrily because an "imposter" has stolen her show.
Bodyguard: "Stop that shuttle! She's the real one... er, I mean, she's an imposter!"
The utter hilarity of Waltfeld's dumbfounded staring at Lacus's fast and professional autograph signing too.
Athrun wakes up and finds Meer in his bed. And then Lunamaria had to come knocking on his door. Hilarity Ensues. After Meer left, Lunamaria was not happy about it so she decides to say some "nice words" to Athrun, leaving Shinn, who happened to be there, very confused.
Cagalli's announcement, just after the outright destruction of Orb, two Lacus Clynes being present on the airwaves at the same time. Gilbert Durandal's "Didn't See That Coming" facial expression is hilarious.
When Meyrin visits Athrun in the sick bay, the following conversation happens:
Meyrin: "Are you feeling okay?"
Kira: "That's the wrong question to ask Athrun, since he'll always say he is."
Athrun: "But I really do feel okay!" (tries to sit up, and winces) "Ow..."
Unintentional but seeing the performance of Earth Alliance mobile suits can be downright hilarious at times. For example seeing 30 Windams being unable to hit a target flying straight at them.
Probably in poor taste, but this troper always ends up grinning during the Meer's Diary bits where she's Fangirling over Athrun. Helped by the clips of their interactions, including Athrun's many freak outs.
As entertainingly pathetic as he is, Yuna gets a lot of good moments, particularly in his interactions with his far more serious (and increasingly irritated) subordinates. Take this example from ZAFT's invasion of ORB after they discover Lord Djibril is hiding there:
Yuna: "Why is this happening? I already told them he isn't here, so WHY ARE THEY STILL ATTACKING US?"
Officer (exasperated): "Because they know you're lying, sir."
And what about the bit when Cagalli returns to center stage?
Cagalli (paraphrased): Yuna, you acknowledge that it's really me?
Episode 48, during the explanation of the Destiny Plan, there's an animation with a chibi Djibril yelling at a chibi Durandal from behind a desk. Then, they receive the cards that apparently determine what job they're suited for. A pair of chibi suited guys then jump Djibril and drag him off, while a third one then installs Durandal in his place. And to add that, when it cuts to some people watching the explanation, the screens do in fact have that animation on them. It's like some kind of humorous propaganda piece thrown into an otherwise serious explanation.