In the scene when the men are fighting the American/Mexican War they show the American flag with 50 stars on it.

Again later, at a dance after Orry Main has been hurt and George Hazzard goes to the dance to meet his soon to be wife the flag on the wall has 50 stars on it also.

These are both in Book 1 episodes 2 or 3.

Anyone with knowledge of American history knows that before the civil war we did not have 50 states

we only had thirteen and if the movie was to be completely accurate they should have used the correct flag.