The setting is Philadelphia, yet the asteroid that killed the dinosaurs is shown hitting the same area. That asteroid landed in modern day Yucatán Peninsula in Mexico.
Most of the music played in the background corresponds to the time frame of the scene. However, at one point in a post 1776 scene, supposedly celebrating an independence day anniversary, the "Stars and Stripes Forever" march by John Phillips Sousa is playing. That song wasn't composed until 1896.
Richard's father at one point early in the film names several cities that he states are along the Pennsylvania Turnpike, when in fact these are all cities that are along Interstate 80 in PA, which hadn't even built at the time.