There are three extra missions in the game, all located in the town of Imasho.

After the event in which you obtain the Red Ring, talk to Ekei. He will say that a woman pickpocket has taken a special item from him. First, seek her out behind the stables. Next, she will be in the second-floor balcony of the bar. After that, she goes to the blacksmith's shop. Finally, she will be back at the first hiding spot. Take the item she gives you to Ekei, and you should receive a technique book.
After the event in which you obtain the Red Ring, talk to a man that is in the shop next to the bar. He will give you chalk. Trade this with Ekei to get a book. Trade the book with Magoichi to get an emblem. Finally, give this to Kotaro in return for a melon. Take the melon to the man. After you rescue Oyu from Gifu Castle, talk to the man's father, who is standing next to him. He will give you a special necklace.
After you rescue Oyu from Gifu Castle, this will be your final opportunity to buy items and receive gold from enemies. Your goal is to clean out the store next to the bar. After this is accomplished, talk to the salesman again, and he will give you a special necklace.