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.
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".
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 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.
When the brothers are cutting their hair and showering, Connor's tattoo is the top half of Jesus and Murphy's is the bottom half. But during the tattooing scene on the boat their tattoos switch briefly until the meeting with Romeo.
After Noah 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.
Noah's hand tattoo looks the same in the flashbacks as it does in present day, which is at least 25 years later. Tattoos fade over time; the earlier ink should have been relatively fresh and crisp-looking.
During the shootout at the Prudential when Conner and Murphy are sliding across the floor while shooting, they fire at least 15 rounds from each of their pistols. However these new pistols of theirs, which are supposed to be Desert Eagle Mark XIX's chambered in .50 AE (though the actual guns used are .357 Magnum Desert Eagles, but the script ID's them as .50 caliber Desert Eagles). The Desert Eagle .50 AE has a magazine capacity of 7 rounds, so Conner and Murphy's pistols would hold a maximum of 8 rounds (7 in the magazine plus an extra round in the chamber), though in the elevator we saw them racking the slide and chambering a round after putting the magazines in, so they most likely only had 7 rounds in each gun. It would of been better for them to keep their Berettas since they hold a maximum of 16 rounds, 15+1 in chamber, it doesn't make sense for them to switch them for pistols that have half the magazine capacity of their old pistols right before attacking a room full of mobsters armed to the teeth.
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.