The credits say that Johannes Brahms's fourth symphony, second movement is heard (in a version by Herbert von Karajan, not Arturo Toscanini as in the film), but it is the fourth movement.
The O'Briens have a fancy ceiling fan with lights attached in their lounge room; these were not available in the '50s.
Mrs. O'Brien's dish-washing liquid comes in a clear plastic container, which wasn't invented until after the '50s.
When young Jack enters the neighbor's house to snoop, there is a brief glimpse of a tuned wind chime which is heard sounding. Tuned wind chimes didn't exist in the 1950s; there were only the un-tuned, jangly type (and very few of those in middle-class Texas homes).
During the prehistoric sequence, explicitly shown to be prior to the event which wiped out dinosaurs, we see a shot of sharks. Then we see a large Manta Ray. The Manta Ray evolved from shark-like ancestors only as recently as 5 million years ago, much too late to coexist with dinosaurs who lived prior to 65 million years ago.
When Mr. O'Brien receives the terrible news at the beginning of the movie by phone, the camera and camera operator are reflected in the handset.