Holly's hair has a big gap in her front bangs when she says her one line, whereas before her bangs were intact. Holly Gilliam did this on purpose in an effort to avoid working on the scene again because she despised the process of filming. It didn't work, and the result is the continuity error.
After the bombing in the mall (when Jill is holding the suspicious package), Sam Lowry gives his coat to a wounded woman and is apprehended shortly after. In the next scene in the back of the paddy-wagon, Sam is wearing the coat again.
In the early scene of the movie, in the Department of Information Retrieval, when the bug falls into the printing machine, we can see that the "Subject for Detention and Interview" forms identify Archibald Tuttle as a "shoe repair operative." This is, in fact, the occupation of the soon-to-be wrongfully identified "Buttle." Archibald Tuttle's occupation is "heating engineer."
When Lowry enters Lint's office, Lint is seen from the side wearing a clean white lab coat. The towel to his left is almost clean. Then Lint turns around to Lawry. All of a sudden coat, its sleeves and towel are bloodied.
When Lint, who has just returned from a 'customer', takes off the bloodied lab coat, it is shown briefly from the inside being soaked with blood. However, there are no blood traces on his vest underneath.
Sam sticks his head in his refrigerator to cool off when his air conditioning breaks. He leaves it open throughout Tuttle's visit, but just before Tuttle leaves the door is shut even though no one closed it.
When Kurtzman is trying to find information about Buttle/Tuttle on his computer, he removes his glasses and sets them on his desk. He then punches a key to spy on his workers. A shot of the employees shows they are watching movies rather than tending to their work. The next shot shows Kurtzman with his glasses back on his face as he angrily takes them off again.
When Sam falls over Jill's truck's hood, she walks around and sees his right foot hanging on top of the grille over the truck's fog/turn lights. But when the angle reverses to show her, his foot is resting on the bumper, in front of the grille.
When Sam Lowry is overwhelmed by the incoming cylinders coming through the pneumatic tubes, he connects the "incoming" pipe to the "outgoing" pipe with a short U-shaped hose. The bend in the hose is far too sharp a turn for any of the cylinders to make it to the "outgoing" pipe.