Continuity mistake: When Tom Hank's men are in the village close to the start of the film, the soldier knocks down the wall accidentally, and the German soldier at the front picks up his weapon and points it (this can be seen from outside the house looking in). Then when it cuts back to all the German soldiers, he's picking and pointing the weapon again. (00:56:20)
Continuity mistake: When the group of soldiers led by Captain Miller are in the village, and the Hill knocks the wall down accidentally, if you notice when Captain Hamill and his two others above shoot them dead, that a lot of the blood gets sprayed onto part of the back wall, but when we see the wall from inside the house, there is hardly any blood at all. (00:56:50)
Continuity mistake: When Miller's men reach the town where the first Ryan is (the wrong one), Miller tells Ryan the bad news about his brothers. When Ryan starts to cry and leans over to his captain the captain's hand is on Ryan's head, but in the following shot it is on the top of his back. (00:59:25)
Continuity mistake: The scene where they are looking for Ryan's dog tag. Doc comments they are laughing in front of all the guys walking by. One of the soldiers looks like Sal Mineo. Frustrated, Tom Hanks walks into the line of soldiers and civilians and starts asking if anybody has seen or knows James Ryan. The same Sal Mineo lookalike walks by him again. (01:15:10)
Continuity mistake: In the scene where all the 101st Airborne troops walk past as Rieben, Jackson, Melish and Miller are joking about the various dog tags, you can see an isolated shot of a young Italian-looking trooper walk past and stare dead at the group. A few minutes later as Miller is yelling at the procession, he shows up again in the background as Miller encounters the soldier whose hearing is impaired because of the grenade. You have to look quickly though, and the image is somewhat blurred. (01:17:10)
Continuity mistake: When Jackson has been given the dog tags to search through he looks for a place to sit. In this scene you see a black box with two yellow boxes at either side in the background. In the next scene the yellow box on the left has magically jumped up onto the black box in order for Jackson to kick it off and sit on it. (01:17:45)
Continuity mistake: When Miller's men are about to take the bunker under the radar tower, they are kneeling on the ground behind some bushes discussing their flanking moves and Jackson is about two feet away from Reiben to his left, but when it cuts Jackson is now behind Reiben. (01:22:35)
Continuity mistake: When they go to find Private Ryan there are eight of them, when they go to a French town and Caparzo picks up the little girl and he gets killed there are seven, right? Wrong. A few scenes later, the camera shows all eight of them marching on to the next town, only in a far away camera shot so it's hard to see. (01:23:11)
Continuity mistake: When Upham is hiding behind a cow while his squad rushes the communication tower/bunker, he uses a sniper scope to see his squad mates. Upham holds the scope differently every time. The two knobs would first be at north/west, and the next shot would be south/east. This will change several times until Captain Miller tells him to get the gear. (01:24:20)
Continuity mistake: At the end of the Radar Station Battle, Miller is yelling for Upham to bring their gear. As told he does. Watch carefully. Just as he picks up the gear, he has a green strap on his chest. when you see a shot of him running, the strap is gone. (01:25:10)
Continuity mistake: In the scene where Tom Hanks releases the German POW, he ties a black blindfold around the prisoner's eyes. Notice how narrow the blindfold looks. In the next shot Upham is guiding the prisoner and instructing him, and the blindfold all of a sudden becomes very broad. (01:34:00)
Continuity mistake: In the scene where Miller tries to persuade Ryan to go back home, watch their shadows on the bridge, they change directions throughout the scene because they were shot at different times of the day. (01:46:00)
Continuity mistake: When Miller has just explained to Ryan that his comrades came to take him back, Miller talks to Horvath alone. While Horvath is talking over his shoulder, you clearly see him moving his hands in the next shot, from an angle just past Miller, his hands are held tight to his gun. (01:48:40)
Continuity mistake: In the scene near the end, when two soldiers are in a row boat packing a bag with explosives, in the overhead shot the guy at the back of the boat puts the oar into the water to his right, but in the following shot from behind the oar is on the other side of the boat. (01:51:40)
Continuity mistake: When the squad and 101st Airborne are waiting for the enemy, Upham, Reiben and Horvath are sitting on some steps outside a building listening to music. In the wide shot Reiben is looking at his fingers but in the following shot his hands are crossed and is holding his arms. (01:56:25)
Continuity mistake: When the two infantries are waiting by the bridge for the enemy, when Reiben, Upham and Horvath are on some steps, Mellish walks up and sits down in front of Reiben. Mellish is taking a puff of his cigarette holding it in his right hand, but in the following shot the cigarette is now in his left hand. (01:57:05)
Continuity mistake: When Miller and Ryan are talking outside a cafe (I think), Miller grabs a chair, sits down in front of Ryan and puts his right hand on top of his left, but in the following shot his left hand is on top of his right. (01:58:35)
Continuity mistake: In the scene when they defend the bridge in Ramelle there is a soldier who wants to attach a stick-bomb at a German tank. When he walks out to the tank you see that he is wearing a beige uniform. In the next shot you see that the uniform has changed into a dark green, and you also see that it is a puppet that explodes. (02:08:15)
Continuity mistake: When Mellish is in the house with Henderson, and Henderson shoots at the wall, just after this shot, the camera pans back to the two soldiers, if you look at the fireplace and chair, it looks like they are covered with dust and dirt, but in the overhead shot of the two soldiers, the fireplace and chair look brand new. (02:16:50)
Continuity mistake: In the Belltower in Ramelle where Jackson and Parker are shooting away, there is one scene where you see Parker running out of .30 caliber ammunition. One second the MG uses a belt with ammunition, in the close up, you see the more modern disintegrating link.
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.