An observer directly powering a dropper or dispenser will only detect the initial 'on' state of a button or pressure plate, it will not detect the change to the 'off' state. this results in the dropper/dispenser being only powered once.

If there is a block (previously or when fixed) or redstone between the observer and the dropper it will be powered twice.

In the picture, pushing the button on the observer to the left will cycle the dispenser below it twice. The button on the observer to the right will activate the dispenser only once.