> 1) let you out (drop charges) and expose the public purse to wrongful imprisonment damages,
> 2) take it to trial and lose, also exposing the public purse to the same damages,
If a doctor makes a mistake, he or she is liable (in addition to the hospital). In the case of wrongful imprisonment, there should be exposed liability for the officers too. They are the ones who make the judgement call to arrest someone based on the information they have and the threat they perceive. If they fail at that and end up causing a net harm to individuals, they should be bearing (within reasonable limits) responsibility for that.
But it takes more than a simple mistake to be able to bring a suit against a doctor, doesn't it? If they misdiagnose, but reasonably, or if complications occur but the doctor was following reasonable medical methods, then they aren't liable, no?
If the police get a call that someone is being robbed, then pick someone up that matches the description that was jogging along a block away, the person may turn out to just be someone somewhat similar that was jogging. Imposing a penalty on the officers, department, prosecutors, etc for failing to convict this innocent person doesn't seem like something that would particularly improve the course of justice.
Certainly it would be an unfortunate situation, but I'm not sure it should be something actionable without showing the arrest itself was intended to harass them, rather than being a case of reasonable mistaken identity.
> 2) take it to trial and lose, also exposing the public purse to the same damages,
If a doctor makes a mistake, he or she is liable (in addition to the hospital). In the case of wrongful imprisonment, there should be exposed liability for the officers too. They are the ones who make the judgement call to arrest someone based on the information they have and the threat they perceive. If they fail at that and end up causing a net harm to individuals, they should be bearing (within reasonable limits) responsibility for that.