Other mistake: The day after the Academy Awards, there is tall corn in the fields and the kids are dressed for warm weather. The Academy Awards are in March, not a warm, corn-growing time in Indiana.
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.
Continuity mistake: The cake Howard's mom has in the car is different from the cake at the reception when the ladies are talking.
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.
Continuity mistake: Right before Emily and Cameron dance in the street there is a shot of the front of the bar. The cars in front of the bar are different from the rest of the scene.
Continuity mistake: After Howard crashes on his bike and he is sitting down talking to Peter there is a big wet spot on his left knee in one shot that is gone in the next.