For the scene where Pam was hung up on a meathook, Teri McMinn was held there by nylon rope tied between her legs. The position ending up being extremely painful for her, and the screaming Pam does in the scene is genuine pain on the part of Teri.
When Leatherface cuts Sally's finger so Grandpa can drink her blood, the device attached to the knife that was supposed to squirt stage blood broke. Gunnar Hansen, already breaking down from having to film the scene (see Sanity Slippage), proceeded to cut Marilyn Burns' finger open for real in order to get the scene done.
Most of the actors didn't actually meet Gunnar Hansen, let alone see him in costume, before their first (which is also usually their last) scene with him. Additionally, there was only one Leatherface outfit and they didn't dare wash it, so Hansen was in the same outfit for weeks in hot Texas weather, making the other actors physically repulsed by his, um, aroma.
The Red Stapler: Inverted. According to Edwin Neal (Nubbins/Hitchhiker), Texas State Troopers actually shook his hand and thanked him for causing crime to drop 18%; apparently the message audiences took away from the movie was "Don't pick up hitchhikers".
Sanity Slippage / Troubled Production: Happened for real while filming the infamous dinner scene. The food rotted under the filming lights and created a horrific smell, combined with that scene filming for 27 straight hours in 110 degree Texas weather, actually drove the actors a bit nuts. The DVD commentary has Gunnar Hansen eerily recounting how he genuinely wanted to kill Marilyn Burns for a few seconds after being ordered to by his "brother." Vietnam veteran Edwin Neal (Hitchhiker) even describes it as worse than anything he went through during the war.