The number of banknotes given to the married couple should be a odd number, as superstitious people believe that the couple might separate if the number can be divided in two.
Do not stick your chopsticks vertically into a bowl of rice, as this is used in Buddhist funerary ceremonies.
It is usually said that people should avoid the number "4" for gifts. Like in China and Korea, 4 is pronounced the same way as "death". However, it seems that very few Japanese people really care about this superstition nowadays.
Some shops, cafes or department stores provide plastic covers for umbrellas. Make sure not to enter with a dripping wet umbrella without one.