Impersonating a police officer

I always assumed that impersonating a police officer was probably a fairly serious crime. Perhaps it is. But it's also apparently effectively legal in many states in some situations. In Mother Jones' reporting on BP's hiring of off-duty police officers for private security work, Mac McClelland reports:

Louisiana police don't have any right to tell you you can't walk onto a public beach (even to, as Esman puts it, "roll around in sticky gunky tar that I'll never be able to get off—if I want to, that's my right"). However, they do have the right to mislead you about who they're really working for. In Louisiana, as in many places, it's legal for police officers to wear their uniforms regardless of whether they're acting in an official capacity or working for a private corporation. Which is why Andrew Wheelan, the environmentalist mentioned above, was unaware that the cop who pressured him to stop filming a BP building and later pulled him over so that a BP official could question him wasn't on duty at the time.