When Liber8 are interrogating the mayor Valentine's arms go from by her sides to folded. In a later scene the same thing happens with Emily when she is talking to Kellog in the street. On neither occasion do we see them fold their arms.
Mayor-elect Jim Martin asks Dillon to call him a cab, which Dillon refuses to do. Yet, when Martin was a mayoral candidate, he always had access to a Towncar with a dedicated driver. Now as mayor-elect, he has to resort to public transportation and calls for an ambulance? What a preposterous plot hole.