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.
His smell reportedly got so bad that no one wanted to eat lunch with him, further isolating him from the rest of the cast, even his own "family."
In real life, Gunnar Hansen was regarded by many as an incredibly nice guy. While preparing for the role and trying to develop mannerisms for Leatherface, he became a volunteer for a school for special needs kids.
Gunnar Hansen strongly disliked Paul A. Partain when they worked together on set, because Partain tried to stay in character as the whiny, complaining Franklin during shooting. When he got to know Partain after filming had wrapped, they became close friends.
No Budget: As mentioned on the main page, the film only had a budget of $140,000.
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.
Troubled Production: Filming went reasonably smoothly for the most part, but its third act seemed to be trying to make up for that.
First, lead actress Marilyn Burns proved completely unable to convincingly keep ahead of Gunnar Hansen as Leatherface while he was chasing her through the woods, forcing Hansen to run much slower than he actually could, and even resorting in one shot to pointlessly cutting up tree branches to let Burns widen the gap between them. There was also an incident where Hansen slipped on the wet grass and lost his grip on the still-running chainsaw, which flew up in the air and then came down point-first just inches from his head.
For the scene where Sally's finger is cut for the Grandfather to suck on, the device to spurt fake blood wouldn't work. Thus, what you're watching in that scene is Marilyn Burns actually getting her finger sliced open. Though they thankfully didn't go as far as to make the guy playing Grandfather suck on her real bleeding finger, and there's a quite noticeable edit before he starts sucking.
And then came the worst part of all with the climactic dinner scene. All the food on the table quickly rotted under the filming lights, and the room's poor ventilation made the stink even worse, raising it to genuinely health-threatening levels. Several of the actors suffered genuine Sanity Slippage and took Tobe Hooper's direction as meaning they really were their characters, not exactly the result you want when most of them were playing cannibalistic murderers. Edwin Neal, who played the Hitchhiker, had just come home from the Vietnam War and described filming this scene as worse than anything the Viet Cong put him through. After it was all over, the rest of the crew were all furious at Hooper and he's said it took years for any of them to cool off.