Alright, nevermind. I finally got past the mission. And I figured out what was causing the blue arrows not to disappear from the current payphone and move to the next.
If I parked my car too close to the pay phone, hopped out, and went and talked to the phone, there was no audio from the cop. So after the convo the arrow would remain on the payphone. So instead of pulling up right next to the phone, I would leave the car out in the street and run up to the phone. That way the audio would pop in during the convo and the arrow would disappear from the current phone and move to the next.