Luke and Emmy are tempted to pull off a mantle that's covering some kind of relic.
Emmy: I want to pull it off...
Luke: Shall we pull it off?
Layton: Don't pull it off.
In fact, most conversations that happen just by clicking three times on the same item are pretty funny, especially as Luke begins to open up to Layton and Emmy.
There was another similar conversation like that...
Luke: Oh, a snail!
Emmy: Ew, a snail...
Layton: Hm, a snail.
After solving a puzzle about apples, the professor comments that if the puzzle had been any more difficult, it might have given him applepsy. The pun is hilarious enough on its own for how bad it is, but Luke's face seals the deal.
Barton when having to develop film on behalf of Emmy (who wants him to do it ASAP):
Barton: I'm not sure what kind of film development technique ASAP is, but I'll do it!
Aunt Taffy sticks to her policy of giving candy just to children that it annoys the hell out of Emmy. Emmy tries so hard to get one small candy, but the old woman is always thinking she's trying to trick her with statements that imply Emmy wants the candy. And if you do keep bugging her, it ends with Emmy having run around the market to get candy from her.
Of course, Aunt Taffy is so against giving candy to anyone except children that Luke's response is, "So you won't give any to me, then?" (Keep in mind that Luke is a child who thinks he's an adult.)
The entirety of Luke's door puzzle. Emmy decides the easiest way to solve the puzzle is roundhouse kicking the door down.
Layton: Emmy...please don't do that. I don't want to explain to Clark that we broke down his son's door because we couldn't solve a puzzle.
"Put the back of the back back so that the back's back is facing back. (beat) Professor, I think my brain just exploded."
"Professor, this reminds me of a puzzle... from an insane asylum."