When the Roman starts the record playing, the music begins before the needle touches the record, and continues while the needle is in the outside band where there is no sound. The music continues to play as the scene shifts, and the needle suddenly is in the middle of the record.
After the forklift incident when the brothers say their prayer and then cross themselves, they go in the incorrect order. The correct order is: head, middle, left shoulder, right shoulder, but the brothers switch the right and left shoulder.
During the meeting of the Dons, Yakavetta states that the Saints killed his father, then goes on to say "mi Padrino" which means my godfather. Clearly a contradiction, as a son would never refer to his father as "godfather" even within the "families".
When Detective Bloom describes the killing in the hotel, Jimmy the Gopher hears the story from inside the panic room, though in the beginning of the film Gorgeous George had to push the intercom button to talk from outside, which did not happen during Bloom's explanation.
After Il Duce and the Roman have their conversation, the Roman starts the record again, setting the needle about one half inch from the edge. After the following gun fight the record player winds down to a stop, and the needle is at the beginning of the record again.
During the shootout replay at the bar, with Eunice walking down the middle of the mobsters, you can see the blood packs behind several of the guys' shirts and the mini-explosions that go off when they are triggered.
In the final tête-à-tête between Il Duce and The Roman in the garden atrium, there are occasional reflections of a little blue-green monitor in each lens of each character's sunglasses, likely a dialogue teleprompter.
When Eunice has her pistol in Gorgeous George's face, you hear her cocking the hammer. The pistol is a Para LDA and is double action only. You cannot cock the hammer. In fact the very next scene, the hammer is still down.
In the opening crime scene, S.A. Bloom suggests that the perp was short because the exit wounds were lower on the face than that of the "Saints", however, (in that scenario) someone taller would most likely have a downward trajectory while a shorter person would aim more more level, thus resulting in higher exit wounds.
When Eunice is walking down the table between the brothers in the Yakavetta hit scene, she can be seen firing her Colt Single Action Army revolver 7 to 8 times, despite the Colt only holding 6 rounds. But she isn't really at the shootout. She wanted to "see it with fresh eyes," and is only imagining herself there with the brothers, so it doesn't matter how many bullets she fired.