In the beginning of the film, PFC Winchell's commanding officer tosses a file to him, but he leaves without picking it up. In the next shot, he is walking up the stairs carrying the file.
In the weight room when Baker is gossiping about Winchell, Winchell is pumping weights in a continuous movement. But a shot from Winchell's perspective shows his arms down with no apparent movement.
When Pvt. Barry Winchell reports to SSG Diaz he is told by Diaz that he will be assigned as the assistant gunner for the 40mm grenade launcher. This could be a reference to the Mk-19 40mm belt fed grenade launcher. However, we later see Pvt Winchell carrying an M-203 40mm grenade launcher. The M-203 is not a crew served weapon, it is operated by a single soldier and therefore doesn't need an assistant to operate it.
During the first scene in the nightclub, when Calpernia leans backwards over the table, the prosthetic breast appliance worn by Lee Pace visibly puckers and separates twice.