When Tom Hanks told them to stop looking at the dog tags...
The scene where they stop at the camp and two of the guys start looking at the deceased's dog tags always bugged me. For one, it really bothered me how they grabbed a handful, looked at them and then threw them back into the box which they were still checking. That was such a stupid thing to do.
But the main reason that scene bugged me was how Tom Hanks insisted that Ryan's dog tags wouldn't be in there and they should keep going without even checking them all. He was in charge of the mission, and those boy's lives; he would not just do something so reckless based on nothing but a hunch. I realize that Tom Hanks really wanted to believe that Ryan was still alive but he wouldn't just not check the tags in the box.