While Arthur takes Eddie's blood and Mason is yelling at him, the position of the bloody rag used to wipe Eddie's face clean as well as the EEG wiring changes positions between shots.
At the party, right before Eddie arrives, Arthur is getting ice from the bathtub and the toilet seat is up. A moment later, the toilet seat is down.
When Emily steps through the window frame, her hair is dry and perfectly done. In the next camera angle, her hair is sopping wet.
When Eddie is in the isolation tank and Arthur monitors him, a printer periodically produces Eddie's EEG in a paper strip that grows every second, with a characteristic noise repeating. When the shot changes, the noise is still heard; thus, when the printer is seen again, the strip should have grown a lot. However, the strip is approximately the same length.
The recording which Emily listens to of Eddie's first drug-induced tank trip isn't the same as the original dialog. Some of the wording is changed, and the loud primal "grunt" which alarmed both Mason and Arthur has been replaced with a sound much more resembling that of a monkey.
During the experiment where Emily is present, they try to control the conditions as much as possible, and are even watching Jessup through a monitor screen when he's in the tank. This is impossible, as recording video would require a source of light, and, by definition, there cannot be a light source in a sensory deprivation tank. (Even night vision goggles / cameras require a minimal source of light; they don't work in absolute dark.)
During Arthur's narration of his report on Eddie's early experiments, he states, "A number of students hallucinated." It would not pass academic standards for a doctor to write a report and neglect to mention a more specific number of test subjects whose experiences are so pertinent to the study overall.
When the Brujo tells Eccheverria that he'll allow Eddie to participate in the ceremony, he walks off. Although in only a matter of seconds he's far enough away that they have to run quite a distance to catch up to him to ask him some further questions, this is consistent with other literary and screen depictions of shamans having "spooky" abilities, sure-footedness, and being surprisingly limber for their age. Rather than an error in continuity, this seems to be a dramatic device.
The story has Emily, an anthropologist, often acting like a "hard science" scientist (think biologists, chemists, medical doctors). Anthropology is a "soft science", a social science. However, this may be due to Eddie's influence and his lack of social graces; he talks to her as though she shared his "hard science" knowledge and assumptions.
During the hallucination sequence in the cave, the pyrotechnic charges underneath the mushroom-shaped rock are visible as it elevates, as is the wire lifting it up.
Emily is shown as being very pale in her early scenes. All of her scenes take place in either New York or Boston. However, when she returns to Eddie, her skin tone is exactly the same as it was in the first half of the movie; she is supposed to have been in Africa for several months studying wild primates, but nowhere is she seen to have either a tan or sunburns.
The introductory story is set in 1967, but exterior shots of the streets show a VW Rabbit and a Plymouth Volare, both 1970s cars.