In the section of the movie where the refugees travel to the US, there is a scene that shows a Delta Aircraft (767-300ER) landing. The livery shown on the aircraft is the current livery used from 2008-present, also known as the "Upward and Onward" scheme, changed because of the merger with Northwest Airlines. The time that the refugees would have been traveling to the US is before the merger, so that livery should not have been used. The proper livery would be the either the "Colors in Motion" scheme, used from 2000 until the merger with Northwest Airlines, or the Ron Allen scheme, which was the livery used before 2000.
In a scene where the brothers are discussing Cheerios cereals, one says Banana Nut Cheerios which only existed after 2009.
In a scene where Carrie is browsing the web, the laptop which she is using is using Windows XP which for the time period in 2001 would not have existed as yet.
After Jeremiah quits his grocery job and goes back to the employment agency, the phone number in the window is a St Louis area code, not Kansas City.
When the refugees first arrive in Kansas City and mention needing to meet an escort by the baggage claim, they descend an escalator. MCI (Kansas City's primary airport) does not have a lower level baggage claim. The airport is three, single-level terminals all with various baggage claims on the same level.