That depends on how obvious the mistreatment of the population is. If the "police" are walking around doing this in broad daylight, while the Paladins are around, I would expect them to put a stop to it. Slavery is unquestionably evil, and executions without a trial would be heavily disapproved of by any Paladin. If there are hints, they might check it out, but I wouldn't expect them to launch a heavy investigation in this case unless they find evidence of the application of the "law" in this province.
By the way, I'd like to say I think this character is acting far more like a Chaotic character than a Lawful character. He doesn't hold trials, he doesn't hold his men accountable for their actions, and he doesn't seem to have a very organized approach to the way he runs the town. He also seems to view the town as his own personal playground, which again likens him more to a Chaotic character than a Lawful character, in my opinion. Judging from the actions you've described here, I'd say he's either NE or CE.
Also, I don't see why you wouldn't immediately drop him to evil for infractions like this. Executions without a trial is tantamount to murder, and enslaving someone is one of the few crimes comprable with the taking of a life. This isn't a few petty acts of evil, this is evil that warrants execution or life imprisonment in most systems of justice in both real and fantasy words.