When Jack says, "So I'm to be the triple pillar of the world transformed into a strumpet's fool" he is paraphrasing lines from Act I Scene I of Shakespeare's "Antony and Cleopatra". Antony's friends Demetrious and Philo speak similar lines while lamenting how Cleopatra has Antony wrapped around her finger and how he has been neglecting his duties as a Roman general.
When they race back home to check on Jane the house number is briefly visible as "221B" the house number of another famous consulting detective. Sherlock Holmes.
Jack seems very tempted by Phryne and vice versa when Phryne is encouraging Jack to put on the Antony costume and begins taking off Jack's tie. In her playful and seductive way she says, "come on Jack, just one gaudy night". Jack looks lustfully at Phyne, who is standing close and replies suggestively, "If you want a real Roman soldier...". During this ensuing pregnant pause they exchange a long lustful look, deescalated when Jack disappointingly continues, "then I'll take it from here.".