When the pace car pulls into the pits at the race in Darlington, you can clearly see that the cars are Busch grand national cars, not the Winston cup cars.
During many of the races shown in the movie shots from the wrong track are shown. For example, the caption at the bottom of the screen for one race claimed they were at Martinsville speedway, but a shot was shown from Daytona speedway (in one shot you can even see DAYTONA USA painted on the wall!)
No team could use a single race car for an entire NASCAR season, especially when it is being wrecked every week.
At one point a crew chief (I think Rowdy's) warns his driver to lay off the car in front of him, because the rear bumper was likely to come off and go right through the radiator. The "bumpers" on Winston Cup cars are made of flimsy plastic or fiberglass, and wouldn't go through an aluminum radiator if fired from a cannon!