I think I would go with
1) KC instead of province on turn 11.
2) Turn 13 - don't play the lookout, Forge it with the coppers/curses into something! Oh, and keep enough coin to buy another KC.
Those are the two things that I'm pretty sure were definite mistakes. (I'm also not convinced the lookout opening was right, but it definitely worked for you here, since you drew 3P for an alchemist anyway, and then used lookout to hit 2 estates...)
But the first one was a big one. You greened too early, and that let you lose the Mountebank war. For example, on turn 13, you start with Alchemist, Alchemist, Province, [stuff]. You do pretty well anyway - but you don't draw your whole deck and you miss your potion, your alchemist stack falls apart, and you never get it going again. If that early province was a king's court, you would have had a chance to do KC->KC->(alchemists and mountebank), probably drawing your whole deck, forging away everything, not just some stuff, and KC-mountebanking him.