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.
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.
Most people would certainly notice a 30+-story clock shop that suddenly terminates at nothing and think at least something was awry.
It's mentioned several times how the sky is very hazy in future London due to industrialization. It's entirely possible that everything above the second floor is obscured by this.
Also, the game apparently insinuates that if you live in London, you never leave. Otherwise that fake Future London would be discovered rather quickly.
How does Claire know how she died?? She isn't a ghost! If she was really just randomly launched into the future, then how the heck does she know about everything that's going on???
It is known that the Professor Layton games have lots of plot holes so let that one slide. If one is so stubborn, then it is safe to presume that Claire was launched into the future before the explosion got her so of course she would know how she will die because she can literally see it coming.
Where did Clive get all the material for a skyscraper sized mecha? And how did he build that thing without anyone noticing?