The Portokalos house has Corinthian columns which are said to be like those of the Parthenon. In fact, the Parthenon's columns are Doric, which are much older and simpler than the elaborate Corinthian columns.
In the travel agency, Toula is on the phone telling a customer that their reservation is PNR. That is incorrect travel agent lingo - a PNR *is* the reservation itself (it stands for Passenger Name record) - she should have said your seats are confirmed.
When Toula decides to sit at the table full of blondes at college, she places her brown bag lunch on the table then sits down. In the next shot, she picks up her lunch bag and sets it on the table in front of her again before opening it.
Later, in the same sequence, she is shown holding an invitation. When Nicki shows her the earrings, she sets the invitation down, but when she says, "I never saw any bridesmaids dresses," she is holding it again.
During Ian and Toula's first date, in the restaurant, there is a medium shot over Toula's left shoulder, and there is no coffee cup on the table. In the next shot, a coffee cup appears on the table near Toula's left arm.
The goof item below may give away important plot points.
Errors in geography
In the very last scene, where Toula, Ian, and their daughter are walking down the street to Greek School, just before fade to black a TTC bus (Toronto Transit) can be seen driving across the intersection.