Factual error: The image of Faro Portugal seen in episode 10 of season 2 is actually an image of "Ponta Delgada", a city on an island several hundred miles away.
Factual error: When Lance Hunter is about to be captured by the military at the beginning of the episode, the troops arrive in a convoy of humvees. The humvees all have Virginia license plates on them, but U.S. Military tactical vehicles do not use license plates. Even if we assume they were using Hummer H1s instead of tactical humvees (commonly used as a substitute on TV and in movies when producers can't get military humvees), military-owned non-tactical vehicles do use license plates, but they don't use state license plates as seen here. Instead, they use official U.S. Government license plates like the ones on the Ford sedan Hunter was dropped off from prior to meeting General Talbot. (00:01:55)
Purpose in the Machine - S3-E2
Factual error: When examining the sand, Bobbi states "According to carbon dating..." Fitz finishes by saying "It's a billion years older than the earth." However, carbon dating is only good at determining the age of something to about 60,000 years old. The only thing carbon dating could tell about the sand is that it is 60,000 years old or older. It certainly couldn't determine that the sand was 5 billion years old.
Chosen answer: Coulson believes he was resuscitated then sent to Tahiti to recuperate. "A magical place," he calls it. But in the "Agents of S.H.I.E.L.D." episode "The Magical Place", Coulson, through a mind-reading machine, learns that he was treated by S.H.I.E.L.D. and a fake memory of Tahiti was placed as a "mask" of sorts over the painful memory of the operation, which involved a drug seemingly of alien origin to repair the damage, coupled with a lot of morally dubious surgery.