I believe the reason he has a right to publish this work is because he is not profiting from their likeness. He is profiting from his work of criticism. (Edit: a sibling comment points out that Ohio exempts audiovisual and political works)

Also, as a public servant in official duty, in a place where they found themselves likely to be recorded, they had no reasonable expectation of privacy.

I disagree, mostly because it isn't hard to get fringe cases. Drunk folks, folks with memory issues, and so on. Even if they break in, I don't think this is the sort of thing they should face public ridicule for.

I think the homeowner has the right because the folks breaking in are cops. If a cop cannot handle these facets of their job being public, they should act better. A cop in uniform is a public figure, even if they are in a private residence. An ununiformed cop is a public figure if they are doing cop stuff, especially if they are in your house.

They should be acting like someone is always watching. They should be able to handle being told bad words from people. They should be expected to always act professional. That is part of the standard we set for call center employees, after all, and we should expect folks that can ruin other people's lives to live up to better standards.