Stephanie M. answered 04/28/15
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"the competence," because otherwise you've changed from singular tense (an officer) to plural (their) to singular again (his).
It may be better to say something like "An officer must be competent enough to perform his duties." or "An officer must have the competency to perform his duties."
"businesses'," since there are multiple businesses and they each possess their windows (hence the apostrophe).