When Danny and Jackie are arresting auxiliary officer Galatis in his bedroom, the camera shows a poster recruiting former military personnel to apply for the NYPD. However, the poster says "Attention Military Personal" instead of "Personnel".
During the shoot out one of the ESU officers is firing an AR type rifle. With each round the weapon jumps up with apparent recoil. An AR type rifle in the hands of a trained shooter has almost zero recoil.
Jamie is having trouble paying his student loans. However, as a Harvard graduate he should have known about the Public Service Loan Forgiveness program and been on their income based plan with affordable payments. The program is known to have many faults now, but there were few reasons for him to not sign up back then.