For all sports, replay that takes more than 30 seconds. If it is not obvious after 30, go with what the officials called. For basketball I hate when a defender knocks the ball out of an offensive player's hand and it goes out of bounds and they say the offensive player touched it last. The defender caused the ball to go out of bounds. Give it to the offensive player.
Also when a shot is so bad it gets lodged between the rim and the back board and they call it a jump. The ball should to to the other team if the shot was that bad. (unless it was tipped by the other team, which rarely happens)