The bite marks on the grilled cheese sandwich keep changing.
On the first morning in Safford when Linda and David are preparing to look for jobs, Linda leaves in a striped sweater vest and skirt. When she returns that evening, she is wearing a striped, long-sleeved sweater and slacks.
The hair color, thickness, and grooming of Paul Dunn, David's boss, changes radically several times in a matter of moments.
They never would have been able to pull into New York City and find a Winnebago-sized parking space right in front of the ad agency just like that.
During the final cross-country montage, as they are approaching New York City, the Winnebago drives up the exit ramp from the Lincoln Tunnel with Manhattan visible in the background. That road is taking them away from Manhattan, into New Jersey, not to Manhattan.
In the final montage, between Newnan, Georgia (where David tosses the map out the window), and the approach to Atlanta, there is a shot of a water tower shaped like a giant peach. They would likely pass this water tower on their journey, but it is located in Gaffney, South Carolina, and not southwest of Atlanta as implied.
When the characters supposedly are arriving in New York, it can be seen from the position of the Empire State Building that they are travelling the wrong way.
During the cross-country trip heading east entering Texas, the Visitors Center is on the wrong side of the state. I-10 starts at mile marker 1 in West Texas. The Visitors Center at mile maker 879 is near the Louisiana border heading west into Texas from Louisiana.
It would be very difficult to make it from Arizona to New York in a gas-guzzling Winnebago, plus the cost of meals and tolls, on $800 and his crossing-guard pay.