The phone number written on the wall ends 362. Later, when Shruti is writing the address on the paper it appears to end 326. @ 2:13:00 in the movie.
While Barfi! is running, a 'Vodafone" ad board is seen, even though blurred. The film is set in the 1970s.
In the Police station, Mr. Sen Gupta is wearing an 'Abercrombie & Fitch' t-shirt which wasn't available in India until 2010.
(at around 1h 55 mins) Calcutta was renamed Kolkata in 2001, but 'Kolkata Municipal' can be seen on the left side of Barfi.