Tony was still engaged to Melissa so it doesn't make sense that Roger set up a double date with two girls from the Miss Universe competition (it's doubtful Melissa would have been okay with that). This episode fits better if watched after Jeannie and the Marriage Caper (1965).
The auctioneer sells Tony for some shekels. Shekels were not used in "ancient Persia."
It was established in the previous episode that Jeannie was in the bottle for 2,000 years, which would put her life as a human at somewhere prior to 35 BCE. Jeannie's parents make reference to Allah, the Islamic term for the deity, but that time period predates the coming of Islam by some 660 years.
In the wedding hall, a woman says to Tony, "May Allah bless you," many centuries before the founding of Islam.