The lipstick imprint on Ellie's forehead changes shape, density, and position.
The film starts with Ellie stating that she had just turned 15 in October, but in a scene set that same month, Max tells Billy that Ellie is "almost 16."
When the Chrysler Windsor convertible is shown driving past Janie's Café (a Longmont Co. location) there is a 1964 Ford parked on the street. There should not be a 1964 car here since the movie is set in early fall 1962.
When Max and Elie arrive at Eleonor Roosevelt's house, there is a blooming crabapple tree or cherry tree on its landscape, that's not possible because it's November.
Max and Ellie decided to leave on a Friday morning, skipping school to get a head start before anyone notices they're gone. However, the date displayed on screen on the night of their first motel stay is October 22, 1962, which was a Monday.
When Bob and Billy stop for lunch at a restaurant and sit by the front window, the same three cars are seen in the background, driving one way and, a few seconds later, the other way. Several times each.
The morning after Annabelle was taken to the hospital with a fever, Bob puts water in a kettle and puts the kettle on a gas stove and turns the dial to supposedly ignite the flame to heat the water for coffee. Then he turns around and leans back on the front of the stove with his right hand resting on the edge right next to, if not over, where the flame should be burning the bottom of the kettle. He keeps his hand there for several seconds without a problem. As Ellie leaves the kitchen, a side angle shot of Bob leaning on the stove reveals that the flame is not on at all.
Daisy says she hasn't danced seriously since she was 19, and says it like it was a long time ago. She then claims she was the original actress cast as Louise, the lead role in the stage musical "Gypsy." However, she is saying this in October 1962 and that play debuted on Broadway in May of 1959, which is a mere three and a half years in the past. Thus Daisy's age would be 22 or 23. Jessica Alba was 32 or 33 at the time of filming and her character is the aunt of a 15 year old girl, so there seems to be a discrepancy with the character's time line.
The date of the Denver newspaper Ellie glances at is October 27, 1962. Assuming their departure date was October 22 (as shown on screen), it took them five days to drive roughly 1300 miles, which is only about 260 miles per day. Assuming they're on the road an average of 8 hours per day, that's less than 35 miles per hour. If they were concerned about getting away far enough before their absence was noted, they sure weren't driving like it.
When they arrive at the Paramount Theater in the first week of November 1962, a sign is visible in a second story window above the store to the left of the theater entrance that reads "I [heart] (+2 illegible words)." The "I [heart]" ideographic concept did not begin until after the "I [heart] N Y" logo was created in 1977.
On her letter to Eleanor Roosevelt in October of 1962, Max writes her return address abbreviating her state as "CA" but at that time the standard postal abbreviations for California were either "Cal." or "Calif." The two-letter "CA" abbreviation was not adopted until October 1963.
When Billy picks up Bob after Bob's pickup breaks down, there are two houses in the background with designs that are clearly newer than 1962.
In a photo of the group in front of the Graceland guard station gates, the musical notes and Elvis figurines on the gate are painted black. In 1962, the gates were all white.
When they drive through Times Square in the first week of November 1962 they pass the Criterion Theater with a marquee advertising "Lawrence of Arabia." That film's U.S. premiere was indeed at the Criterion, but not until mid-December 1962.
In a travel montage meant to summarize their progress from New Mexico to Kentucky, a series of postcards are included, but the sequence doesn't make geographical sense, going from Texas to Missouri to Oklahoma to Tennessee to Kentucky. Oklahoma should have been before Missouri.
After they arrive in Colorado, Max talks about her Aunt Daisy living in Las Vegas, Nevada and Ellie corrects her that it's actually Las Vegas, New Mexico. Since they drove through Zion National Park, they must have gone through Las Vegas, Nevada first. That would have been the time for Max to be confused. Not one or two days and 700+ miles later.