When Frasier and Niles are oohing over less-than-manly work tools, Martin says, "This is why I never took home movies!." Yet in Season 7, Episode 1 "Mama Mia," the boys had Martin's old home movies converted to video so he could watch them when they visit the old family cabin. In fact, the home movies are shown as Martin, Fraser, and Niles watch them.
Frasier and Niles are repairing the ball-cock assembly in the toilet, which they have to install by "threading through the tank hole." So clearly the toilet tank is empty. They then proceed to flush the toilet without ever turning the water back on or giving the tank a chance to fill.
While Billy is telling Frasier how he use to torment him, Billy is using a screwdriver to work on the inside of the toilet bowl. He is obviously not working on anything because there are no moving components on the inside of a toilet bowl that require a screwdriver or any other tools.