1. The # of phone calls to the police about a crime are not necessarily indicative of how common that crime is. If people think the police won't do anything, they're less likely to bother calling (I see this often in my area with things like stolen bikes and catalytic converters... people often don't bother getting a police report unless their insurance requires it).
2. Throughout the 2010s the crime rate trended downward
3. Crime rates can have seasonal variations (but this can vary based upon location and type of crime)
Skimming through the paper, #1 wasn't addressed at all.
For #2, the paper compared the 2015 data against 2014. I don't think they did anything to compensate for annual trends in crime rate. In other words, if the crime rate in Des Moines, Iowa lowered at the same time, is that actually a ripple effect from NYPD's actions? Or are both cities just part of a larger downward trend that we saw coming out of the 2009 recession?
For #3, they actually took temperature and precipitation into account which was cool.