After the successful Trinity test in 1945, people in a crowd are holding small US flags with 50 stars on them (offset rows). At the time there were only 48 states and the flag had 48 stars in even rows. The 50 star flag didn’t exist until 1960, after Alaska and Hawaii were made states in 1959.
When Jessica walks from the house to the barn at the end, she is wearing knee high brown boots. By the time she reaches the barn they have been replaced with court shoes.
At the end when Brian jumps onto the semi truck to save Vince if you look closely at the back of Brian’s pants you can clearly see the safety cable that holds him onto the semi truck. (01:26:17)