Deliberate mistake: When Howard walks up to the front of the church he is alone. Suddenly, when his bride comes out, the best man, maid of honor and flower girl are at the front of the church. This happens despite the fact that the music flows and there was not time for the others to enter.
Factual error: The movie opens with the Academy Awards, which as everyone knows are held no later than late March. Then Howard's wedding is no less than a week later, at which point he accidentally outs himself and is subsequently fired. It's clear that the kids' graduation is no more than a week or two later (made especially clear by the fact that Cameron, rushing to town, gets there the same night of the wedding and then is still there at graduation.) But high school graduations are in June or, at the earliest, May - which last time I checked was more than a week or two after the end of March.
Plot hole: Why would the press converge on Greenleaf to begin with. Nobody but the residents of the town know that Howard still thinks that he is straight. Why would press people from across the US think that there was a story there? Dozens of people get thanked every year at the Oscars and the press certainly doesn't do follow up stories on every single one of them.
Continuity mistake: When Kevin Kline goes to school the day after the awards show, the press chase him to one of the school doors. When the scene is shot from outside, the door opens into the building and he is pushing it open, but immediately after when the shot is from inside of the school and he is closing the door, it opens outwards and he is pulling it closed.