I'm sorry, every time I read a comparison between secret police and plain clothes officers, I feel obligated to post this rant:
If you believe that "plainclothes officers" are the same as secret police, you know jack shit about the Gestapo, the Stasi and MSS or even ICE, all of which are undoubtedly secret police forces.
Officers in plain clothes are just that, they are a part of the normal law-enforcement operation, operate under the law and report to normal chiefs, normal prosecutors and normal courts, inside constitutional limits. Even if the justice system is rigged, racist, out of whack, and heavily skewed, they still operate inside of it, they're just sneaky about it.
Secret police on the other hand are often embedded as special units in organizations that otherwise operate as intelligence services and are therefore not easily recognizable to outsiders. A secret police force is an entirely different animal than just a couple of sneaky police officers. They are a quintessential feature of authoritarian regimes. Either de facto or even de jure unbound by constitutional limits, they are a tool of political repression and preemptive, unlawful violence. They are the ones who disappear people, they often run their own secret prisons and interrogation centers.
The fact that ICE is more and more morphing into a secret police service is FAR more alarming than the existence of plain clothes officers in the US.