Earlier quoted context omitted.
I absolutely think you should be able to record the police. But following them around is potentially unsafe for everyone involved. It's also a good way to harass good people out of the profession (the worse a job is, the more you have to scrape the bottom of the barrel to fill it). In addition, it absolutely can be a misdemeanor to harass people, government employee or not. No one deserves to be insulted. The problem…
How is following police unsafe for everyone involved?
I can think of a number if situations in a number of jobs I have had were people following me around could have been dangerous (farm hand, concrete work etc).