Hand Signals
The hand signals used in Saving Private Ryan are largely inaccurate and were not in use during World War II.
The film's military advisor was Dale Dye, a U.S. Marine Corps veteran who had served during the Vietnam War. It is possible that Dye used hand signals that he was familiar with, and was not aware that they were not used during WW2.
Similarly inaccurate hand signals were used in the Band of Brothers mini-series, which Dye also consulted on.