It's his mother Gillian who initiates the intercourse; Jimmy tries to get out of bed but she stops him and says they're not doing anything wrong:
A train passes and he says goodnight and goes to kiss her forehead.
She tilts her head upward and kisses her son open mouthed. She tells
him that there is nothing wrong with any of it and repeats this phrase
as he returns her passionate kisses. The noise of the train continues
as the mother and son have sex.
WRT breaking any laws: I have no idea.
I don't think there's an Oedipus complex, since it seems to me Jimmy is merely indulging his mother; he himself has relationships with women. It is his mother who has a warped sense of love and sexuality; don't forget that when Jimmy was an infant, she kissed his genitals to show her affection. Also, the day after Jimmy and his mother have sex, he enlists with the army, claiming he's an orphan. (Though it is clear that Oedipus is one of the themes on the minds of the writers.)
The "Jacobean" comment refers back to an earlier scene:
The professor tells the class that it is part of the Jacobean style to
depict Italy as corrupt and the women as whores while the men are
panderers. He asks for a more specific interpretation of the scene and
Jimmy offers one; his mother taught him things that are not of use and
that he is hungry for the riches of those around him. The professor
congratulates Jimmy and ends the tutorial
To me it sounds as a roundabout way of calling Jimmy's mother a whore. Also, the book they were discussing in class, The White Devil, is written by John Webster, "an English Jacobean dramatist".