Usually you need either a pull-up or a pull-down resistors for you input pins. With my old K3NG CW Keyer I forgot the details and thought I put some resistors on the board. But actually, the internal pull-up resistors were used for which some care is necessary for your code like:
pinMode(pin, INPUT); // set pin to input digitalWrite(pin, HIGH); // turn on pullup resistors
Or more simply,
pinMode(pin, INPUT_PULLUP);
Anyway, a single touch to the paddle causes several interrupts since there is no circuit implemented on the board to take care of the contact bounce.