DC police Dep't
Don Kates forwards this link to a story ("A list that makes it more difficult to put criminals away") noting that DC prosecutors have a list of officers under investigation, somewhere over a hundred at any one time, and plan their cases around it (make sure a confession is witnessed by someone not on the list, etc). From the story, "under investigation" isn't just "someone complained he was impolite or used too much force," but more like "he's implicated in a robbery." That'd make sense, since you probably wouldn't waste time planning a case around the fact that an officer was accused of being rude, nor of using force (unless the case was, say, assault on an officer).
In forwarding it, Don states that during a time in the 1990s, the DC PD suspended background checks on applicants, and a number of felons became officers. And that it's not the list that makes it hard to put criminals away, it's the conduct that got an officer on the list.
The DC PD has 3600 sworn officers, so 100+ is a bit under 3% of the force.