Hey, I helped edit the blog post. Definitely agree that the different spiky behaviors are driven by data collection, but that's the beauty of real-world datasets! It would be interesting to learn if it was bulk first-of-month reporting, that crimes where the day wasn't specified get marked as the first, or some other phenomenon. The next step might be to interview police officers and ask :-)
Here's the top crimes broken down by the first of the month vs the average for the rest of the month - some crimes are only reported (or never reported) on the first of the month, and "FRAUD" for example is twice as likely to be the first of the month: https://sli.mg/lHjo83