Right after Brenda leaves him, and after Dale finishes in third place to finish in the money, Dale returns home and puts a stack of $20 bills on the table. The design of the twenties are the new design, created in 2003, while the scene takes place in the 1970s.
Though the cars used in re-enacting the races of the 1970s and 1980s are authentically correct, the track billboards are not. You can see the current Pepsi logo on one of the billboards. Also, Sunoco (the current fuel supplier of NASCAR since 2003) has their logos on the track when the fuel supplier of NASCAR during Earnhardt's era was 76.
Many cars depicted in the 2001 Daytona 500 are incorrect in terms of body styles and paint schemes. Most noticeable are the cars of Jeff Gordon, Bobby Labonte, and Rusty Wallace. Gordon's car sports the old rainbow color scheme when 2001 was the first year his car sported the blue/red flame paint scheme. Bobby Labonte's Interstate Batteries car is Chevrolet Monte Carlo, his actual 2001 car was a Pontiac. Wallace's car in the film is a 1998 Ford Taurus using the old blue/white Miller Lite paint scheme (the actual car was a 2001 with an all-blue Miller Lite paint scheme).
There was a shot of the RV park during a race identified as 1990. There was an orange Tony Stewart flag in that shot. Tony Stewart didn't start driving the #20 Home Depot Car in Winston Cup until 1999.
At the end of the movie, where Dale Earnheardt is shown at his last race at Daytona, Bobby Labonte is shown driving a Cheverolet Monte Carlo. Labonte was, in fact, driving a Pontiac Grand Prix in that race, and did not drive the Monte Carlo until after Earnheardt's death.
Later on when Dale is in his late teens and racing the pink k-2 Ford, there are scenes with the front bumper, then without, then with, then without. You'll have to rerun it a couple of times using the pause & rewind, but you'll notice.