When Caleb is done shaving, he exits the bathroom drying his now-clean face with a towel. As he picks up his shirt, he glances over at the monitor to see Nathan conversing with Ava and then tearing up her picture. When the camera returns to Caleb, he still has shaving cream on his face.
When Ava pulls the knife from Nathan's back she is seen using her left hand to pull it out, the hand that was ripped off by Nathan minutes earlier.
Caleb should have been able to get out when he caused the power outage by inserting his key card into the computer, because he programmed the security system to unlock everything when a power outage would occur.
Caleb reset all the doors to be unlocked when the power failed. However, at the end when he is locked in his room by Ava, the power fails, and his door remains locked.
Throughout the movie, Ava speaks with an American accent. However, when she asks personal questions of Caleb, upon asking "What about your family?", she uses a very distinct British accent.
The writers incorrectly attributed the quote, "I am become death, destroyer of worlds," to J. Robert Oppenheimer. The quote is from the Baghavad Ghita. J. Robert Oppenheimer wrote that he said it after the first A-bomb test. His coworkers who were present with him at the viewing reported that all Oppenheimer said was, "It works."
At the beginning of the film, the helicopter pilot tells Caleb that they have been flying over Nathan's estate for the past two hours. Assuming that they are travelling at a cruising speed of 130 knots and that the airport they took off from is situated immediately on the edge of Nathan's estate, then they have already flown 260 nautical miles. As the Eurocopter EC130 has a range of 330 nm and the pilot did not refuel at the spot where he dropped Caleb off, it would therefore not have enough fuel to make it back to its point of departure.
Nathan's facility cannot have so much optical fiber cables (OFC) to get to the moon and lasso it. Simple math to calculate the total length of walls to contain so much cabling proves this.
When Ava and Kyoko meet in the corridor, there are masks on the wall. At the end of the scene, the masks are gone. Correction: The camera angle is not a reverse shot along the same corridor with the masks. The camera has moved to where Kyoto is standing, turned 90 degrees right and is looking down the corridor she came from. When Nathan finds them, he is looking from the other end of the corridor where Kyoto came from.
When Ava has put on clothes/"skin", her breasts become notably smaller. This is not a goof. Ava merely exchanges one "shell" for another. Her original gray breast plate was designed to make it look like she had large breasts underneath it. But being an android with only a mechanical body, Ava obviously has no actual breasts in the first place.
The design of Nathan's security system is extremely unsafe: real secure environments would have battery backups for the key-cards, some doors that fail open for safety, and so on. However it's established very early in the movie that Nathan designed the security system himself, and that Nathan is a paranoid alcoholic who can't conceive of his own fallibility. Of course he designed the security system this way.
When Ava presses her drawing against the glass to show it to Caleb, in one shot it slightly slips. Apparently the contact pressure of her hand changes over time to the point where the paper starts moving. Nathan designed his android bodies to be human-like, up to and including making small errors like this; it is entirely consistent with her behavior in the rest of the movie.
Caleb had already reprogrammed the security protocols when Nathan was drunk. Thus he did not need to get him drunk again on the day of Ava's escape, and Ava could have escaped earlier during the penultimate power cut. Caleb still needed Nathan to get drunk so that he and Ava could actually escape unseen, otherwise Nathan could still have prevented them from escaping somehow.
After Ava puts on Jade's "skin," the olive skin becomes very Caucasian and Jade's "landing strip" becomes a small thatch.
Every time the power goes down, the designer Nathan has no option to see what happens. This is ludicrous. The eyes and ears of Ava, the artificial intelligence system would themselves be accessible to Nathan as a camera and microphone.
Ava uses induction to charge her batteries. This suggests there is some device in the walls, floor, or ceiling of her room Manning this possible. It's unclear how she intends to charge her batteries after escaping.
A good designer such as Nathan would be able to control the AI system using a wireless interface. When Ava escapes, he would have simply logged in to her and shut her down. This shows that the writers knew nothing about Computer Science.
Passing the Turing test indicates an intelligence indistinguishable from a human intelligence. Exactly what such a result implies is a matter of debate and the conclusion that the characters in the film draw - that passing would imply consciousness - is one of many accepted schools of thought on the subject.
In an analogy, Nathan says that Caleb should pretend he's "Star Trek's" Captain Kirk and "Engage (his) intellect." However, it was not Star Trek's Kirk, but rather Captain Jean Luc Picard of "Star Trek: The Next Generation" who was known for speaking the command, "Engage!"