- Public sex as it relates to public nudity: Most people assume that no ban on public sex would mean no ban on public nudity, although you can have one without the other. Some think seeing naked people is qualitatively different than seeing sexual acts. There's disagreement over whether we can make principled distinctions as to what body parts can be banned from public view.
- Health concerns: Many seem convinced that allowing public sex would result in increased transmission of STIs or that there might be health risks to other users of public spaces. Does the risk of increasing STI rates or of making public spaces less sanitary justify the regulation? (With respect to the latter, it might apply equally to public nudity, at least the below-the-waist variety.)
- Public sex and sexual harassment: While some have attacked the analogy of sex to speech as invalid because people are rarely attempting to communicate to others when they perform sex acts in public, on the occasions when they do, it may be an attempt to harass others (the popular example is the dirty old guy on the subway). Does allowing public sex mean allowing this? It looks to me like you're damned if you do and damned if you don't: if you're intentionally trying to make someone watch you have sex, it might be harassment and thus bannable, but if you're totally oblivious to the people around then it's not communicative and thus bannable.
- Public sex and minors: While some think seeing sex in public traumatizes kids, this doesn't hold cross-culturally. Public sex might mean more minors would be sexually active, but if it coincided with a switch to a liberal (read: European) view of sexuality it might be accompanied by more responsible behavior.
- Public sex and offensiveness: At least one person claims that public acts can be regulated if they are offensive to the community without this being oppressive. Others have disagreed. Whether or not offensiveness is a legitimate ground in general for exercising the police power has come under fire, especially with respect to speech.
UPDATE: I will be moderating the comments section. If you are not substantively contributing to our discussion of the harm principle's application to regulation of public sex or nudity, you will be deleted. Please read the main comment thread before weighing in. Many of your ideas have already been discussed in some detail.