These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Horror: How many people must've died during Clive's rampage on London? Every step he took crushed homes beneath his giant mecha's feet, and he was firing cannons all over the place the entire time, not to mention the huge chunk of the city he destroyed while making a hole for his mecha to rise from beneath the earth. Unless every single one of the homes destroyed happened to be empty at the time, countless lives must've been lost. And stranger yet is that nobody called Clive out on that.
Well, he does get arrested at the end.
Forget the buildings that were already destroyed, London has a giant sinkhole in it's center. Who knows how big that thing will get and how much of London it will consume.
Considering what he wanted to do and his motivation, he is pretty hypocritical, and it's a wonder why Layton didn't point to it and ask him how many more people has he made to be just like him.
And at the end, Claire knows she has to go back to get blown up.
Fridge Brilliance: The statue of the young boy and a man in a top hat was actually Clive's tribute to Layton's kindness.
The puzzle in which two friends meet, with one having a fast watch he thinks is slow and the other having the opposite problem, takes on new significance when you consider that the puzzle giver, one of the kidnapped scientists, thinks he's in the future, but is actually in the present.
Fridge Logic: Most people would certainly notice a 30+-story clock shop that suddenly terminates at nothing and think at least something was awry.
Also, the game apparently insinuates that if you live in London, you never leave. Otherwise that fake Future London would be discovered rather quickly.
Where did Clive get all the material for a skyscraper sized mecha? And how did he build that thing without anyone noticing?
Nightmare Fuel: Dimitri's flashback in which he discovers Claire's dead body. All you see is her arm, but it's still unsettling, especially when one remembers this is a game for children.
A mentally unbalanced Clive using a mobile fortress to devastate London. It's not made clear if the area was evacuated, and if it wasn't, he may have killed a large number of people, although it's not brought up in-game.
Subject 3's backstory. He was a cute little bunny, abandoned and orphaned, before he was captured and sold to scientists and subjected to a number of torturous experiments.
Tear Jerker: The ending. First, getting to know why Clive did all this - he lost his parents in a time machine accident. Then, the scene where Claire says goodbye to the professor. Note: Layton actually cries and takes off his hat during this scene. And finally... Luke leaving because his father got a new job, which is even more sad after you've played the 4th game and realize that Layton is also losing one of his best friends - Clark.
This exchange, when Luke and Layton are parting ways and Luke begins to cry
Layton: Now Luke, a gentleman does not make a scene in public.
Luke: I'm sorry, professor. I'm not a gentleman yet! *hugs him*
Dmitri's flashback to the day Claire died, after he arrived too late. God, he looks so broken during the entire scene.