Just after Cam Brady (Will Ferrell) punches the baby's face, the different newscasts use actual footage of the punch from the film itself (slow motion, baby's perspective, different angles...) and not moving images from what a video-camera of the News would take.
After Cam is arrested, a reporter approaches him and asks "You were charged with drunk driving. Is it true you blew a 1.4?" A BAC of 1.4 would almost surely be lethal; at the very least, Cam would surely have been hospitalized, not walking around talking with reporters. It's possible that the character simply misspoke, meaning instead to say 0.14 which is above the legal limit for driving in all states and a much more believable BAC value.
At the end, when accepting the congressional office that Cam Brady has declined, Marty Huggins says that he is going to "...end Daylight Savings Time. I hate when it gets dark early." In fact, DST extends the daylight so that it does not get dark early, but later.
At the end of the movie, Marty Huggins reveals a giant scar running across his torso, an injury he received as a very young child; photos showing a teenage Marty Huggins in a swim suit do not show this scar.
When Tim Wattley is talking to Cam after interrupting their family time and sending his kids to their room we see Mitzy walking down the hall away from them. However, in the very next shot she is right next to Marty again.
In the first debate scene, when Marty and Cam first walk out onto the stage, the two podiums are the same height. However, after they shake hands and go to their respective podiums, Marty's is considerably higher than Cam's.
At the party where the election results were revealed, there is a flag on the table in front of Marty that goes from being flat to being slightly pushed over and back to flat again without ever being touched by Marty or his wife.
At the very beginning of the movie, an on-screen quote is attributed to H. Ross Perot ("War has rules. Mud wrestling has rules. Politics has no rules"), and refers to him as a 1988 Presidential candidate. Perot ran for President twice: first in 1992 and again in 1996, the year he made the comment used in the film. He did not run in 1988.
The goof items below may give away important plot points.
Under North Carolina law, Cam Brady cannot withdraw his name from the election on the day of the general election. After being declared the nominee of a political party, the deadline to withdraw one's candidacy is 30 days prior to the general election, and requires a written request to be submitted to the board of elections which certified his nomination (NC GS §163-113). As Representative-Elect, Brady could resign from his elected office, but Huggins would not automatically win the seat. The Governor would be forced to call a Special Election to elect a new Congressman (NC GS §163-13).
When Cam Brady is attempting to sleep with Mitzi Huggins, he puts down his iPhone in order to film and exploit it. If you look at the bottom icon of the screen that links to the photo library the thumbnail shows that Mitzi and Cam already sitting together. Clearly this was from a take not used in the film and the previous attempt to record was not deleted beforehand.