Factual error: In this episode we see Blithe get shot in the neck and are told that he died in 1948. In reality he was shot in the shoulder and survived. He later served in Korea and was promoted to master sergeant as well as receiving the paratrooper of the year award. Blithe died in 1967 while on active duty in Germany.
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.
Revealing mistake: In "The Breaking Point," Lipton is narrating the bombardment of the woods right outside of Foy. Just before he says, "What I saw that day," at 30:55, you see a section of a tree explode, but when the debris (i.e. the splinters of wood and snow) clears you see that the "blown up" section of the tree is unharmed.
Factual error: David Webster is shown to be training as part of Easy Company and is present among their number when Lt Meehan informs them that the invasion has been postponed. Webster actually trained with Fox Company and made the jump into Normandy as a member of the Battalion Headquarters Company. He transferred to Easy Company after D-Day.
Other mistake: When Heffron is taking his throw at darts, he states that he needs a "double seven". When he takes the throw, the dart goes into the treble eight (an earlier close-up confirms that the board has the standard Gamlin configuration), yet, from the reaction he gets, he's made the throw he was going for.
Visible crew/equipment: When the patrol is on its way, one of the boats tilts over and some soldiers are screaming they can't swim. At some point during that scene there is a wide shot with in the background the other side and a skylight. Right in the middle of that shot on the other side you can see a man walking away wearing a orange vest or jacket of some sorts. Might be the pyro-guy.
xx:xx:xxSven van Leeuwen
Continuity mistake: In part 5 when Easy company surprises the two sleeping German companies, with Winters leading the charge. Winters crosses the berm and a sleeping German stands up, and gets shot. Winters then shoots off 9 more rounds (2 too many), then reloads, drops to one knee and only shoots 6 rounds (2 too few), and in both cases the clip ejects as if it were a normal 8 round firing sequence.