Ashima is dressing to meet the prospective groom and tosses the end of her sari over her right shoulder; next scene it is neatly done over her left shoulder.
At the baby girl's ceremony, the position of the dollar on the tray changes from front to back to front again between shots.
When the Ganguli family visits Calcutta in 1977 one of the advertisements on the streets is for the Calcutta based newspaper "Telegraph". The Telegraph was established in 1982.
The Gangulis' dark green Volvo 240 sedan has a New York license plate up front and a California one on the back, when the movie is set in New York and a registered vehicle in the state of New York must have a license plate from the state in which it is registered.
The baby used to portray the newborn Gogol is not a newborn. He is clearly at least 2-3 months old, if not older.
The vandalized mailbox: the flag being up normally indicates to the postman that there is mail to be picked up and is lowed by the postman when the mail is picked up. also, the pattern of the graffiti indicates it was put on first with the flag down; then the name was stuck on and the flag raised.
In one of the scenes, on the Airport flight display board, Delhi is misspelled as 'Dehli'
Several anachronisms show up in the 1977 flashback sequences
showing Calcutta (Kolkata); the railway station shows a sign for Indusind Bank which was not established until the late 1990s; there is a building of The Telegraph which was not launched till 1982; and there are shots of several bridges and buildings which are only recent additions to the city.
Early in the film when Gogol's mother and father are sitting together and one of them is holding a letter that they plan to mail to India, there are 2 U.S. stamps on the envelope. These stamps are current (2007) stamps, yet the letters are being mailed in the late 1970's or early 1980's.
While in the International Arrivals area of JFK Airport, Gogol focuses on the holographic photos/art lining the hallway; this is a modern decoration of that area (and that technology wasn't prevalent ~20 years ago).
The hardcover Pantheon edition/translation of Gogol's stories that Ashoke inscribes to his son and gives him as a graduation present in 1995 was not published until 1998.
When the parents go to New York in 1977, the license plates on the cars are the current blue and white plates (with the state of New York in the middle). The color of the plates in New York in 1977 were orange with dark blue letters and numbers.
When the family is in the airport (leaving the US), they're in the International Arrivals (not Departures) area of JFK Airport.
After the family reaches Kolkata by air they are shown traveling in a taxi on the Howrah bridge entering the city, but one does not have to cross the bridge to enter the city from the airport because both the airport and the city lie on the same side of the river Ganga.