(at around 49 mins) Pastor Phil, beginning the church Nativity Pageant, says, "Are we ready to see the results of that immaculate conception?" implying that the "results" are the birth of Jesus. The title "Immaculate Conception" refers not to Jesus but to his mother the Virgin Mary, without Original Sin (thus, Immaculate) in the womb of her mother, Saint Anne. Mixing up these two events is a common misconception.
Brad referred to Burma as an Asian "island nation". It is not an island: its southern border is its only coastal border (although this might be due to the fact that he's lying to his parents about going to Burma - his lie is so ill-conceived that he doesn't even know this basic fact).
When "Ken" and "Daphne" were having sex in the bathroom, "Daphne" ripped "Ken's" shirt off. You can see the buttons flying. Yet in the next scene when they are coming out of the bathroom, "Ken's" shirt was buttoned up nicely.
When Brad returns and he and Kate are talking outside the front door, her makeup changes style back and forth multiple times. Eyeliner/no undereye circles/reddish lipstick to no eyeliner/undereye circles/pinkish lipstick and back again.
Based on their bar scene and apartment interior, Kate and Brad appear to live in swanky SF apartment, yet when they depart to San Francisco Airport (SFO) they drive over the Golden Gate Bridge which is North of San Francisco; SFO is to the South.
During the Taboo game, Denver answers "What is the capital of China?" with "Hong Kong". This is part of the joke. Denver and his wife, who obviously have little education, think that Hong Kong is the capital of China. The point of the game was for Denver to guess that "Hong Kong" was the answer on the card, which he did. The point of the scene was to demonstrate how well they knew each other and how poorly Kate and Brad knew each other. The fact that Denver got "Hong Kong" from "What is the capital of China?" helped to make that scene funny.
While Kate and Brad are arguing in the car, going to their final Christmas at her father's, there is an obvious re-shoot because at some points she is wearing a wig and then in the next shot it is back to her normal hair. It goes back and forth this way throughout the scene.
San Francisco gets fog in the summer, not winter. In winter, it might be raining, but never foggy. When it isn't raining in the winter, it's usually quite clear and sunny. The scenes on the Golden Gate Bridge were obviously filmed in the summer.
The goof item below may give away important plot points.
Due to federal privacy laws, the hospital wouldn't be allowed to identify Brad and Kate by name without written consent. They also wouldn't have allowed the reporter to "surprise" them in their hospital room.