In the garage, when Donnie tells Maggie that his job is eating him alive, 2 Hess trucks (one from 1994, one from 1995) are visible behind Donnie, on the upper left. Krylon paint, which was not available in the 1970s, is also visible.
In 1970s New York, sawhorse-style traffic safety barricades were pieced together out of wood (like real sawhorses), then painted yellow or orange, sometimes with stripes. One street scene shows a white plastic model with applied reflective orange stripes, first used in the mid-1990s.
In one scene, the feds use Sennheiser HD25 headphones for phone taps and to listen to Donnie's recordings. These headphones were released by Sennheiser in 1988.
These headphones are very popular among sound men in cinema and television hence why they are probably in this scene.
At the beginning, the 'Big Boss' arrives in a black Lincoln. From the front first shot, the Lincoln is much older than the model in the next shot, as the car pulls up to the curb. The front turn signals are from both the older Lincoln and the much newer Lincoln.
When Brasco tries to call his wife, and discovers that the number has been disconnected, he dials area code 212, which is Manhattan. Pistone lives in Clifton, New Jersey; at the time, the area code was 201.
In the car, Lefty shows Donnie a newspaper photo of the Carmine Galante crime scene. In the next scene, they pull up to Sonny's club, and small piles of snow are on the sidewalk. Galante was killed in July 1979, so there should be no snow on the ground.
When Lefty makes the coq au vin, he dredges the chicken in flour before browning it (highly unusual and not the classic method, as it often results in blackened flour), then sprinkles a few drops of brandy on the chicken immediately after putting it in the pan (in reality, this is done later, after the chicken has browned on all sides), which results in a flame far too big and too yellow to have been caused by a mere splash of brandy.
At one point, ELO's "Don't Bring Me Down" is playing in the background. Later in the movie, while in Florida, Sonny Black reads in the paper that John Wayne died. John Wayne died June 11, 1979, and "Don't Bring Me Down" wasn't released until July 21, 1979.
When Donnie is shooting on the firing range, the second shot ends without the pistol's action returning to firing position because the magazine is empty. The shot cuts to the target, which is immediately struck by more bullets.