The trailer shows a battleship exploding and people falling into a pool at what appears to be a party; neither of those things actually appear in the film.
Cole describes himself as a "soldier". A Marine or former Marine would NEVER describe himself or herself as a "soldier", because a "soldier" refers to someone in the Army. A Marine would describe himself or herself as a "Marine".
During the I-Day formation, Donnie Wahlberg (Lt Cmdr Burton) has a mustache as he sits on the stand. This was acknowledged by the director and producers in their commentary on the DVD, and they left it in because you can barely see it and they have several creative ways of explaining away its absence later. However, just the day before he was clean-shaven when he met with Jake at the shipyard.