Instruct your captain to invent something, pause the game, put the game speed up to full, and wait a couple of minutes. Now unpause the game, the captain will have kept inventing during the pause!
When you wish to invent in double quick time, click invent and when your men leave, click on it again. This often makes a catapult almost immediately, but this cheat only works once on each island.
In winter, take a lone captain to the north of the map. Leave him there, but keep an eye on him, because he'll start shearing a sheep. Then, he eats it.