Audio problem: On the beach, a soldier with a B.A.R. puts his arm around Captain Miller's neck and says they don't have a chance. His line carries over to the next shot of Miller unwrapping his Thompson, but we can see that soldier behind Miller, and he's not talking. (00:16:00)
Audio problem: After the Rangers break through the German lines at Normandy, Captain Miller delivers a message on the hand radio. After he turns his back to the camera and stops talking, he continues to move his mouth. (00:24:30)
Audio problem: When the Americans are defending the bridge, there's a scene where the guy with the m1 carbine is shooting his rifle. When he shoots the last round, his rifle "pings". Only the m1 Garand "pings". (02:18:10)
Audio problem: When Ryan and Miller make their way to the bridge, they reload and fire their weapons behind sandbags. Miller begins to fire his Thompson but it jams and we see him try to rack the charging handle to fix it. He then tries to fire again but the gun fails to do so; all while we hear the sound of the Thompson firing. The editors added the sound of it firing despite the fact that it jams in the final cut.
Answer: These were barrage balloons, commonly used during the war. They are used to stop low level bombing and low level fly bys by enemy fighter planes. The cables attached to the balloons are designed to cut through the wings of the aircraft and to bring them down, so any pilot would have to fly above them, and the balloons would also restrict the view from above.