In the days leading up to Monday’s Boston Marathon, “Patriots Day” director Peter Berg had several meetings with the folks at the Boston Athletic Association about the possibility of filming a scene or two on race day. “We’ll be almost invisible,” Berg had told us. “We want to have no impact on the race. Those guys have a lot of work to do.” So we were not surprised to see Mark Wahlberg, dressed as a Boston police officer, discreetly shooting a scene near the finish line Monday. The film crew was long gone by the time the elite runners started showing up. Earlier in the morning, Wahlberg joined Mayor Marty Walsh at the ceremonial Patriots Day flag raising at the Paul Revere statue at the Prado on Hanover Street. . . . Meanwhile, over at Fenway Park, there was an emotional scene as Marathon bombing survivor Jeff Bauman joined actor Jake Gyllenhaal to film a scene for “Stronger” — based on Bauman’s book — and then throw out the first pitch before the Red Sox-Blue Jays game. Gyllenhaal walked onto the field carrying Bauman’s daughter, Nora.