When the characters take Heroin, either injected or snorted, the sequence showing their eyes dilating is inaccurate. Opiates produce a constricting of the pupil. However, the dilating is correct when the characters are using Ecstasy and Cocaine.
(at around 1h 10 mins) Sara is in her apartment wearing her red dress, creeping around trying to avoid her refrigerator, popping her pills and watching herself appear all dressed up on Tappy's show. There is a pot on the stove and her vacuum cleaner in front of the stove. At different cuts in the same scenes, the stove is alternately clean or has pots and items on it, and the vacuum cleaner is there or missing, or changes position. (It is possible that some of these changes occur because Sara is hallucinating.)
When Harry is waiting for Tyrone to return with the drugs, we can see Harry playing with a turntable. The shot of the turntable itself shows Harry's left hand on the record. In the next shot, his right hand is in the turntable.
During electroconvulsive therapy (ECT,) the character is shown as being conscious and suffering greatly, when in reality the procedure is done under anesthesia. The patient is not conscious, nor do they experience discomfort.
When Harry calls Marion from the hospital she picks the phone up with her right hand and puts it on her left ear but when the camera focuses on her it's on her right ear. This is almost certainly a mirror shot, not a mistake.
At two different times during the movie (when Marion, Harry and Tyrone are discussing the possibility of getting heroin from Brody, and when Harry is sitting around waiting for Tyrone to come back with Brody's heroin), records are supposedly playing, but the tone arms are in the 'up' position and the stylus is sitting above the record.
When Marion is leaving Arnold's flat for the first time you can see some parts of the steady cam outlined under her coat. When she catches some wind while leaving the building, the coat is lifted up for some instants and you can actually see them.
When Harry and Marion get in to a fight, at the exact moment that Marion says "You promised me that everything was going to change", the shot is clearly flopped, as indicated by her bangs and the angle of her head compared with the rest of the scene.