Susan says her brother trapped Baby while he was hunting in Brazil. There are no leopards (an African-Asian animal) in Brazil. There are, however, jaguars, which bear a passing resemblance to leopards. The animal shown is clearly a leopard (the telltale being the lack of dots in the center of each "rosette"), and correctly called such, even if the continent of origin is incorrectly named.
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.
When Susan is dragging the wild leopard into the jail house, 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.
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.
Gogarty and Major 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 David and Susan are trying to get Baby off of the roof, the shadows produced by Baby and the chimney are inconsistent with natural lighting. Baby casts a shadow to the left and the chimney casts a shadow to the right.
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.
The goof item below may give away important plot points.
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.