After being recruited (and flirted) to the good side, Roger tells Marth how he really loves Caeda. Marth's response to this is pure silence. We learn in Shadow Dragon's ending that his title is "Still Single".
Shadow Dragon's endings have some funny notes:
Rickard is stated to have returned home. Shortly after, though, it's mentioned that the area around his home was robbed continually.
Minerva helped to make Macedon flourish. Everyone in there wanted her to be queen, but the only one who didn't want to be queen... was herself. This could be ironic or a "Funny Aneurysm" Moment, though, because come Mystery of the Emblem, Minerva is still unwilling to be a queen but takes the position anyway because there's no one else more qualified, and this causes her to be overthrown by Ruckert.
Everything Rickard says in BS Fire Emblem Episode 3. Absolutely everything, especially his dealings with a suspicious Navarre. Seriously. Kazue Ikura's performance as him is absolutely spot on and thoroughly hilarious.
In New Mystery of the Emblem, Luke bemoans the lack of pretty clerics. The others agree that a healer is needed, and Luke is excited—until the recruit turns out to be Wrys. In addition, the entirety of Prologue 6's intro is pretty much a Big Lipped Alligator Moment, but it's hilarious.
All of Malicia's support conversations. All of them.
Xane's third support with My Unit, or at least the first part. He disguises himself as Jagen and claims he's fallen in love with them. Be warned though, massiveMood Whiplash comes next.
While most supports show My Unit as the straight man, his/her conversations with Draug show that not even he/she is above silliness as he/she gets the impression Draug's supposed feats are real (such as taking flight to knock enemies far from the continent). Draug tries to disaude her/him with some impossible training, only to be stunned when he/she says lifting ten people is impossible but not three.
In pre-battle conversations, Caeda will sometimes explain to My Unit that she knows a guy on the other side, complete with flashback to her recruiting them in Shadow Dragon. The reaction of a female My Unit is priceless.
Shadow Dragon's prologue has a couple.
When Cain finally joins the party, he is badly wounded, and Marth tries to encourage him to seek treatment. Jagen cuts Marth off:
Jagen: No, sire, not until we've escaped. Cain, I trust you can put off bleeding to death for just a while longer?
Cain: Of course, sir...I aim to please...
The entire scene around Gordin's recruitment: He's been captured, gagged, and dressed as a Gra soldier in order to provoke Marth into accidentally killing one of his own countrymen. The ruffian holding him captive addresses him only as "Gaggles," and this happens:
Ruffian: Ooh, but sad for you, you look awful dangerous in the uniform...MISTER GRA SOLDIER! Ha! Soon as the prince sees you, 'e'll say, "Yow! It's an enemy ambush!" and that'll be the end of you.