Visible crew/equipment: When Hanks, Damon and company are retreating to the Alamo (across the bridge) the camera pans an overview shot of their retreating and you can see two crew members in the shot - one holding a camera and another supporting member, both wearing white tee shirts on the right part of the screen.
Visible crew/equipment: Before the American soldiers attack the half-track in the field we see Upham walking. Watch at his left shoulder you see a square shadow moving around. It's the shadow of a camera. (01:40:05)
Ronnie BischofVisible crew/equipment: When Reiben, Ryan, and Miller are in the ditch a side angle shows them all on the same frame, if you look carefully to the right and behind some rubble, a blue tent is visible which is revealed in the special features to be the tent that dailies are viewed.
Answer: Most people are not ambidextrous so running left means you'll have shoot left or use the right shoulder to shoot as you're running left which is much harder to do, try this out.