Continuity mistake: In the bootcamp scene where Captain Sobel is yelling at Private Christenson for drinking from his canteen, you see a machine gun resting on Christenson's right shoulder. When the camera angle changes to behind Christenson, the machine gun has suddenly moved onto his other shoulder. This happens quite a few times in this particular scene.
Continuity mistake: When Buckingham is about to be arrested, the camera is looking directly at him. At this angle, his black fur collar is flipped up, covering the neck of his white shirt. When the scene changes to a wide shot behind him, the collar is folded down. (00:35:00 - 00:35:50)
Continuity mistake: After the Battle of Bull Run, Jonas Steele is seen surveying the aftermath. Trouble is, there are a heck of a lot more dead bodies lying around outside the house than there were when the battle was raging, including those of Union soldiers. As the scenes of the battle demonstrated, the Union never actually got as far as the house; all their casualties were incurred on the slopes approaching the house, and then they retreated. (01:53:20 - 01:59:10)
Continuity mistake: During the Medici brothers vs. Marco Bello confrontation near the end of the episode Lorenzo grabs a candlestick to defend himself against Marco Bello's knife - you can even notice a candle slipping off the candlestick. As Marco Bello turns to leave the chamber, however, Lorenzo's hands are empty and the candlestick rests on the table. In the next shot he's holding it again, with the candle sitting atop of the candlestick. (00:47:30)
Continuity mistake: In the scene where John Basilone goes looking for his friend Manny. Basilone has 3rd degree burns on his left forearm and left hand but in the shot he is walking through the jungle holding a pistol tightly in his left hand and his canteen is on his right side as he walks past a group of trees. The next shot he is continuing walking through the jungle but the gun is in his right hand (which isn't burned) and his canteen has also switched sides as he walks past the same group of trees.