Final answer:
The vague phrase in the thesis statement is 'should only', which is subjective and could benefit from additional context to clarify the circumstances in which the police department should hire community-resident officers.
Step-by-step explanation:
The vague word in the thesis statement provided is "should only". The term "should only" is subjective and open to interpretation, which can lead to ambiguity in the statement. To improve the precision of the thesis, it's advisable to specify under what circumstances or contexts the police department should only hire officers who have lived in the community. This would remove vagueness and strengthen the argument being presented.