Whenever Dr. Heiter walks in the room where his patients lie down, a breathing machine can be heard. However, none of the people are connected to a breathing machine with tubes, so this sound doesn't make sense.
When Lindsay spills her drugged glass of water, it is nearly empty, and approximately 3/4 of an inch (one centimeter) of liquid remains. In the next scene, after Dr. Heiter goes downstairs and the woman says, "It's freaking me out!" the glass is half-filled with water again.
When the doctor joins the three for the first time and begins taking photos, he is using a Canon Digital Rebel. When the camera angle changes and shows him taking photographs again, he is shown to be using a Nikon camera.
While the captives climb the spiral staircase, they are bleeding and pools of blood can be seen on many of the steps. However, a moment later when the camera shows a shot of Dr. Heiter at the top of the stairs looking down the hallway by the bedroom, there is not a drop of blood on the floor where the three had crawled.
The human centipede was created in the cellar downstairs and had a lot of difficulty climbing the stairs with the strength of three people. How did Dr. Heiter, being so weak, carry them upstairs and downstairs alone?
The goof item below may give away important plot points.
(at around 51 mins) Where three are in the cage and one of the women reaches to hold her friend's hand, the camera pans to the side. Here, Lindsay is clearly not connected rectum to mouth--her lips are visible with a gap of light between them and Katsuro's butt. Again this is visible in the pool scene and after Katsuro stabs the doctor's feet.