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.
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The dispenser is BUD-powered by the button.(MC-108)
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Unlike MC-11193 this bug is not affected by location, this happens anywhere you build it..
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Edit: Nvm, since observers can't be powered it is BUD powered.
it appears that observers can not be powered themselves, as the redstone below the observer on the left is not powered by the button above it. The only power to the redstone comes from the observer.