As annoying as this must be for them, it could be worse. I worked on an electronic health records system for a couple years, and the state required EHRs to synchronize pediatric vaccination records with their vaccination database, using name dob county of birth as the patient identification. We ran into a case where the vaccination records got merged for two patients with the same name and birthdate/place. The only reason it was caught was because one of the mothers had kept careful track of the medical records herself, and noticed the discrepancy while talking to the doctor. If she hadn't the doctor would have assumed the baby had already had the vaccination.
I hate to think how common this kind of thing might be, without anyone even knowing. It's one thing to have the sorts of problems described in the article. It's a whole new level of terrible when you consider that doctors are making medical decisions impacting your health and life based on records that could be mixed with somebody else's, and you would never know, since patients don't ever look at their own chart.
Having worked in ticket entry I am not super surprised because sometimes it was hard to tell different people's records apart, but it seems like they aren't even trying. How the hell does anyone figure that in that dense of a population there is only one person with a common name like that?
The police department would be the ones at fault with the tickets as they would do the entry and be the ones picking the wrong record. The DMV can only work with what they are given. We had a person whose job it was to untangle these sorts of issues. My personal experience says blame the officers, their handwriting is shit. Possibly New York's ticket form is lacking some fields that would help differentiate who's who as well.