The first scarecrow you encounter in the first set of caverns in Sabine Forest tells you that if you set its head on fire you will have light for the caverns. If you do so, it laughs because you can't set it on fire, and every time you talk to it after that, it's still laughing at you.
In the catacombs, one of the enemies you encounter is called "The Dancing Hands of Bob" or "Mysterious Bob". He confuses your party members by...making them do the boogie. Once you've damaged him enough he does the boogie for the rest of the turn, causing your whole party to boogie as well. To add funny insult to funny injury, despite being a bit tougher than some of the earlier enemies you encounter, he is the only enemy in the whole game who only gives you 1 experience point.
The puzzle where you have to give the maidens their names back. A lot of them have nasty things to say about each other, to hilarious effect.
At one point in the Bonus Dungeon, Erio and Snowe open a door to discover that there is no floor, and fall through. They land in a tiny room that thankfully has a lift. They take the lift back up...and end up coming out a door on the opposite side of the hallway from the one they fell through. Snowe's not amused.
Snowe: Now that just doesn't make sense!
At one point in the Sepulcher, you discover that in one of the rooms there's a spot on the carpet that feels like it has no floor under it. You are given the option of moving aside and pulling back the carpet, or remain standing there. If you choose the latter:
The carpet ripped and you fell down the stairs. Maybe you should have moved.
In "A Demon", Erio's reaction to the really huge staircase in the Eastern Tower.
Erio: THAT'S A LOT OF STAIRS!
The first fight with the Original King ends with him getting dropped through a trap door. The look on Hiante, Relenia, and Astra's faces are priceless.