How did the cops find Jimmy?
I probably wasn't paying enough attention to the movie, but how did the cops find Jimmy Grant, and infer that he helped Miller, and that Miller was the perp? New York is a big city, Miller has tens of thousands of connections, there are many payphones per square mile, and a few cops with a grudge aren't going to have time or permission to sift through all the possible connections, given dozens of fatal motor vehicle accidents a week to deal with.
EDIT: OK, I looked at the scene in Côte's apartment again, and heard the "15 pay phones in three mile" statement. Balderdash. If NYPD is investigating this, it is within the 303 square miles of their jurisdiction, almost all urban with a few strips of park. There were 250 fatal motor vehicle accidents in 2011, 5 per week. So maybe 10% of those are a mystery demanding lots of detectives, etc.
In those 303 square miles, there are 31,000 pay phones, averaging 300 per square mile. If "3 mile" means a 3 mile radius, that is an area of 28 square miles, and there are thousands of pay phones within any 3 mile circle. Over the course of an evening, most of those pay phones would get used a few times, otherwise they would not be there.
Even if they wanted to, could the cops get all the warrants needed, and all the phone records searched, etc., by the next day? I doubt that NYPD would even think about making that kind of rush effort for any single fatality accident. Their job is to help the DA get convictions, and they look for low hanging fruit.
Lazy writing. I can imagine other scenarios that would allow for a dramatic car crash and fire, a pickup by Jimmy, and the license plate picture shenanigans. I use pay phones a few times a year; the writer probably doesn't, or assumes movie audiences don't.