When Harry is getting dressed for his date with Shelly, his brother comes into the room and messes up his hair. Harry tries to straighten it out, but you can still see it sticking up all over. In the very next shot you can see the hair is perfectly combed as if nothing happened.
Harry tells Shelly that he was a popular date in high school because he did "a killer frug." This can't be because the frug was a dance popular in the mid-1960s. The movie takes place in 1972, when Vada is 11. That means she was born in 1961. Her mother died two days after she was born. So Harry was not in high school when the frug was popular.
When Vada and Thomas J. are running away from the bees, Thomas J. says, "Run faster! They're after us!" and Vada responds, "I am running faster!" However, if one watches the scene in slow-motion, it is clear that neither of their lips are moving as they say their lines.