Evidence. Conversations (phone calls are recorded), testimonies, photos, video, unexplained hotel bookings, circumstantial evidence (underwear forgotten, fingerprints, etc.). Just like for any other crime. It's really very easy to prove once the state apparatus gets in motion. — Agustino
Evidence of what, though? It's necessary, first, to define the crime. What kind of conduct constitutes the crime of adultery? What is it that must be proven beyond a reasonable doubt (unless you think that standard should be dispensed with for this new crime)?
Is fornication with someone other than a spouse (I suppose that's redundant) the crime in question, or does the crime of adultery include other conduct?
Let's say police stop a car because one of the rear lights isn't functioning. Speaking with the two occupants, one of the alert officers discovers they're not married. Worse yet, one is a man and one is a woman. His partner (to whom he's not married, by the way) noticed the two occupants were holding hands as he approached the vehicle. Suspecting the couple are engaged in the crime of adultery, the policemen search the vehicle. They find unused condoms in the glove compartment.
Now, if the crime of adultery includes the act of holding hands with a person who is not married to you (well, an adult person, perhaps; holding hands with a minor may be a separate offense), then clearly the search of the car was warranted and the two may be arrested and appropriately charged. But if fornication is required:
May the vehicle be searched?
Is there sufficient evidence to justify arrest?
If there is not sufficient evidence to justify arrest, would there be enough evidence to, for example, search their homes, get their phone records, etc.?
I envy those who will prepare law school/bar exam questions when adultery is made a crime
Once the crime of adultery is adequately defined, we may consider whether
attempted adultery should be a crime as well, whether adultery should be a felony, the range of sentences available, whether more than one instance of adultery should require additional punishment, whether adultery with more than one person should be considered a separate crime, and whether more than one instance of adultery with the same person is a single crime or each instance a crime in itself.
Also, if fornication is a necessary element of the crime of adultery, perhaps conduct which isn't fornication, e.g., kissing, making out, holding hands, hugging in suspicious circumstances, may be made offenses for which a forfeiture is required, if not a lesser sentence.