The Brontosaurus/Apatosaurus skeleton has numerous errors, including the head of a different dinosaur, Camarasaurus. This was not known until certain discoveries were made at least 30 years after the film came out.
At the end of the movie, Susan falls from a platform erected in the center of the back wall. However, in the closer views that follow, the platform is in a different location: about six yards further right, in front of a skeletal exhibit hanging on the wall. In the closing long shot, the platform is back in the center.
The wildcat used in the role of "Baby the leopard" is actually a jaguar, an entirely different species from another continent. Leopards are from Africa; jaguars are native to South America, and occasionally sighted in the American Southwest. Ironically Katherine Hepburn's character says her brother sent it to her from South America, but she still calls it a leopard.
There is no glass in the windshield of David's car. When David and Susan are arguing over the ownership of the car and she drives off, to catch his balance David grabs the frame of the windshield putting his fingers through where the glass should be.
Katharine Hepburn generally didn't handle the leopard. One scene where
this becomes obvious is when Susan has the wild leopard on a leash and is trying to pull him into the jail house. The angle of her end of the leash and the leash attached to the leopard are noticeably different, for they were shot at two different times with a matte.
Gogarty and Maj. Horace Applegate come across the leopard, and Applegate says, "Personally, Gogarty, I think you're a liar!" They start to run away from the leopard, when suddenly part of the leopard's head is transparent. You can see right through to the wall.
When Susan is dragging the wild leopard into the jailhouse, immediately after she utters the words, "Hey David," an obviously mechanical stand-in for Baby (seated on top of the table) is seen turning its head.