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 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.
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.
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 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.
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.
The goof item below may give away important plot points.
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.