The position of the hitch-hiker, in relation to the lorry, as it hits him, changes between shots. Also, the hitch-hiker is an obvious dummy as he is hit; you can see the fake limb attachment on his arm.
When the man at the gas station washes the teenagers' van, the floor around the front of the van is totally wet after he finishes, but as the teenagers pull away, the area around the front of the van is now dry.
When Leatherface chases Sally into the house the first time and she escapes through an upstairs window, he corners her on the stairs and she leaps out a window off the hallway on the second floor. However, when Leatherface appears in the empty window frame after she jumps, he's standing in an attic window with a gable.
As the teenagers pull up into the gas station, look at the position of the gas pump's hose and its shadow. In the next shot, the gas pump's shadow has vanished and the gas pump's hose is positioned differently.
When the group of teenagers pick up the hitchhiker, he goes crazy and cuts Franklin's arm, so they throw him out. As they throw him out, the van-door windows are shut. In the following inside shots, they're open.
When the Hitchhiker has been thrown out of the van and proceeds to chase after, and smear blood on the side of the van, at one point the camera cuts to the inside of the van to show the hitchhiker blowing raspberries through the window at the teenagers. During these perspectives, a clapper board, and a crew member wearing a red t-shirt, can be seen reflected in the window.
The goof items below may give away important plot points.
When Leatherface kills Franklin, blood spatters on his apron and shirt. In the wider shot, as Leatherface lifts the saw above his head and Franklin's flashlight shines on him, old stains are still visible on the apron, but Franklin's blood is gone.
At the end of the film, Leatherface takes a pipe wrench to the face and falls down into a roadside ditch, getting his clothes very dirty. Moments later, when he's doing his macabre chainsaw dance, his clothes are all nice and clean again.
There are two identical meat hooks next to each other in Pam's murder scene, one of which she's skewered upon. However, based on the position of the spare hook, the point of Pam's hook would be above her shoulder and not sticking in her back.