Though the film is set in 1969, the soundtrack features songs that were not released until after 1969. Free's hit song "Alright Now" plays on the radio while introducing Chrissy, Dean, Bailey and Eric. The song was not actually released until the summer of 1970.
The slim design of the chainsaw Leatherface is using would not have been around in 1969. The models of that time period had considerably more bulky engines. The one he had started appearing in the mid '80s.
At the very end of the movie when the car hits the Texas trooper and the guy he pulled over, as the car comes to a stop the bodies are nowhere near the centerline of the highway. As the killer begins to walk away the bodies are closer to the centerline. Then on the last shot of the accident as the killer walks away one of the bodies is completely over the centerline and directly in the middle of the highway.
Near the beginning when Leatherface is being told the slaughterhouse is closed he is chopping meat with the cleaver in his right hand, on one of the close ups it switches to his left hand then in the subsequent longer shot it's back in his right hand.
When Eric and Bailey are escaping, the outside door is clearly wide open. When Hoyt comes down the stairs and sees them, they push the tea lady up against the door. In different shots, the outside door is either closed or ajar when they push her up against the door.
The Texas license plates on the kids' 4x4 have, what appears to be, a month and year validation sticker on either side of the state name. Texas didn't start using such stickers until 1975. The plates should read 19 Texas 69, all indented.
When the 4WD they were driving near the start flips over, just before it gets towed away, you can see the floor automatic transmission lever is in 'park'. when the camera looks out the front window at the old man and tow truck, you can see the shift lever on the steering column in "park" as well.