Before entering the apartment, Danny's hands on the door change position based upon the camera shot.
Before Officer Reagan receives a call from Gabe requesting a meet, it is shown that Reagan and partner Janko are driving an NYPD Ford Crown Victoria. After arriving at the meeting, the vehicle in the background that they come from is an NYPD Chevrolet Impala.
When Danny gets in the car with Whitney near the end, she has just put the car in Drive. He reaches over and takes the key out of the ignition, and then, in a couple of moments, they both get out of the car. At no point do we see anyone put the shifter into Park (or Neutral, for that matter,) so, according to what we see, it is still in the Drive position with nobody in the car.
Jamie and Eddie encounter a corrupt parole officer and investigate the matter themselves. The proper procedure here is to notify that agency so their professional standards or internal affairs unit can investigate. They eventually do this near the end of the show, but in reality they would have done so much sooner.
Reagan and Baez compel a suspect to go to the station for questioning after he had referred them to his lawyer. Even if he had confessed, his confession would be inadmissible since he had requested an attorney. A competent detective would be aware of this legal decision and not waste time as was shown.