Should the prince go down for murder for merely being a Jerkass? Think about it.
Though the movie heavily implies that the prince had killed a woman before, but they were vague enough to make you really wonder about it. He did like to beat women up for sexual reasons.
Although that's as far as words could go in those times: Nobody would dare admit publicly that anyone of royal blood would have killed someone, especially a woman.
And the couple certainly relied a lot on coincidence in order to achieve their goals.
Well, he was staging a coup—those rarely end bloodlessly, and it may have caused the Prince to become a bit of The Caligula.
On the other hand, the illusionist is basically guilty of murder because he wanted to be with the love of his life.
The Habsburg Empire was bad enough already; a coup that puts absolute, totalitarian power into the hands of someone even worse than the current Emperor would be a nightmare. So if they didn't get rid of Leopold, countless more people would suffer or die. The fact that it neatly ties into the Illusionist's personal desires and can be done by an illusion is just a happy coincidence.
Don't forget, the prince was perfectly content to browbeat Uhl into arresting another man for the Duchess's murder on what was surely insufficient and trumped-up evidence. And he outright proclaimed his intention to murder Uhl himself at the end, before realizing it wouldn't suffice to cover up his own intent to seize his father's throne.
Why does the police inspector smile when he realises that he saw a man commit suicide in front of his eyes and had his own life threatened for a lie?
First, the crown prince was still a tremendous jerkass who beat women and there's a good chance he had killed a woman before, so he probably deserved his fate. Second, even if you ignore the whole woman-beating, woman-killing thing (since we don't know for sure that he's killed a woman), he still conspired to overthrow the Emperor. I'm sure the Emperor would be more concerned about that than his love life. Even if you took all the women-beating and killing stuff out of the equation, I'm sure the Emperor would see it fit to see to it his son is punished for conspiracy to commit treason (which was usually punished by the death penalty anyway). That's why he sent the guards to arrest the prince, and that's why the prince committed suicide, so he certainly deserved all that. And third, I don't think it was a happy smile so much as it was a "that son of a bitch, I can't believe I fell for it, I can't believe he pulled it off, all I can do is laugh at this", smile.
He witnessed the greatest illusion ever done, the last and greatest trick by the finest magician in the world. And all Uhl can do is applaud the brazen courage and talent it took to pull it off, right under the nose of Uhl and an entire nation.
Exactly this. He's the witness — the only witness — of the greatest trick ever pulled. And on top of that, the master illusionist respected him enough to give him the blueprints... in essence, to say "you're a worthy enough mind to follow in my steps."
Sometimes, when you're confronted with something so impressive, so ballsy, so incredible, then regardless of what you would otherwise think, all you can really do is laugh. It's a "well played, you devious bastard" thing.
It was less a laugh of genuine humor and moreso out of respect for pulling off a plot so devious, audacious, and daring. Less "Man, the crown prince's suicide is hilarious" and "You slick sonuvabitch, I can't believe you pulled this off."
