Throughout the movie the name "José" is always said with the Hispanic pronunciation of the letter "J" (ho say), but the character is said to be Brazilian. Although Brazil has a Spanish-speaking minority, especially in the borderlands with Argentina and other nations, the nation's primary language is Portuguese, where J is pronounced similar to the French fashion as in Jean or Jacques.
When Holly first looks through Paul's window and sees the 'decorator' leaving him $300 while he sleeps, the ornate gold clock in the background reads 11:30. However just a few minutes later, once Holly is inside the room, we see it again and it now clearly shows 4:30. For the next five minutes, it remains on 4:30, without moving at all.
When Holly sneaks into Paul's apartment to visit the night after they first meet, he is wearing a watch on his right wrist. However, when he states, "They bought what's in that box," while pointing to a box filled with copies of his novel, the watch disappears. It reappears in the next shot.
At the party before she meets Rusty her hair is streaked blonde and has approximately 3 strands of blonde hair running up into her bun. Later the bun and streaks are differently placed. Only two strands running up into the bun.
In interior shots the apartments have windows and a fire escape along the side. In exterior shots there is no space between the building and the one adjacent to it, making such architectural modifications impossible.
When the Tiffany's salesperson mentions Federal tax this is factually correct. There was Federal tax on luxury items in 1960s. You would paid the Federal Excise plus the state tax. Not everything was subject to this excise tax so he was reminding them of this obligation.
(at around 1 min) Just as Holly turns from the Tiffany's window the camera pans left and you can just see a crew/police individual holding back traffic on the street in the distance so they can film the scene.
In the opening scene, Holly's taxi is traveling NORTH on Fifth Avenue to drop her off at Tiffany's. True, the street is deserted because of the early morning hour, but traffic on Fifth Avenue travels SOUTH (downtown).
Early in the movie, Paul cites a review from The New York Times Book Review of his book; he gives the date October 1, 1956. The Times Book Review is a Sunday supplement and is dated for Sundays; October 1, 1956, was a Monday.
The goof items below may give away important plot points.
Near the end of the movie, when Paul and Holly argue, the model year of the Plymouth taxi changes from 1959 (when they first get in) to 1958 (when they stop for Holly to toss out the cat) to 1957 (when Paul orders the cab to stop so he can exit in anger). When Holly relents and jumps out of the cab (that has not moved since Paul got out), it is a 1958 model again.
At the end of the film, Holly puts on nylon stockings in the cab. The left one has a visible run on it, yet the stylish Holly still puts it on. When she steps out of the cab, the run is gone. Then, as she searches for the cat, the nylons seem to disappear and then reappear.
When Holly and Paul are riding in the taxi near the end, the street seen in a rear projection through the back window is a wide, four-lane New York City street. But when the cab stops for Holly to throw the cat out, and in subsequent shots on the street and in the alley, the street is very narrow, barely wide enough for two cars, and clearly a set on the studio back lot.