According to Wikipedia, misdemeanors are OK too, as long as they were committed in the presence of that citizen.
I think the real difference is that the cops have qualified immunity, meaning they aren't at fault even if the arrest turned out to be unjustified, and regular citizens do not.
I think police can be at fault, it's just the individual police officer doesn't typically pay the fine, it's their jurisdiction (city/county), i.e. the citizens.
I don't mean to sound pedantic, just having a conversation.
I think the real difference is that the cops have qualified immunity, meaning they aren't at fault even if the arrest turned out to be unjustified, and regular citizens do not.