adultery is actually a sub chapter of article 134 which is the "general article" or catch all.
Adultery, as a military offense, is difficult to prosecute (legally) for several reasons.
There are three "Elements of Proof" for the offense of Adultery in the Military:
(1) That the accused wrongfully had sexual intercourse with a certain person;
(2) That, at the time, the accused or the other person was married to someone else; and
(3) That, under the circumstances, the conduct of the accused was to the prejudice of good order and discipline in the armed forces or was of a nature to bring discredit upon the armed forces.
Element #2 is usually pretty easy for the government to prove. There is normally sufficient written evidence to prove whether or not someone is legally married. (Many folks will be surprised to learn that in the military, a single person can be charged with the crime of adultery).
Element #1 can be very hard to prove. Remember, a court martial (like civilian court) requires *proof* beyond a reasonable doubt. Proof of sexual intercourse normally requires photographs, a confession of one of the parties involved, an eye-witness, or other legally admissible proof. (The mere fact that someone stayed over at another individuals house, or even slept with them in the same bed is not proof of sexual intercourse.
Element #3, in many cases, can be the most difficult item to prove. The government must show that the individual's conduct had some direct negative impact on the military. This normally would include cases of fraternization (officer & enlisted) or a relationship with another military member, or a military spouse.