Continuity mistake: When Fitz is examining Aida's head, Mack hands him a bottle of beer. He sets the beer on the table and the beer magically twists itself about. It isn't much and it's easy to miss. It's only a few centimeters or so. (00:38:30)
Continuity mistake: When the Chairperson calls the meeting to order and wants to swear in Daisy, you see Senator Nadeer is already sitting next to him. In the next shot, as Daisy is standing up, Nadeer is taking her seat.
Continuity mistake: When Daisy is hugging Jemma after proving they're both human, Daisy's right arm is hooked entirely around Jemma's neck. There's an angle change and a lens flare (possibly to help cover the cut) and Daisy's right arm is now at 90°, with her hand on Jemma's left shoulder. (00:21:15)
Continuity mistake: When Daisy and May knock on the door of the SHIELD contact, the agent opened the door outward. Later when they were under attack, May dragged the agent in, and Daisy closed the door from inside. (00:17:39)
Continuity mistake: When Fitz and his dad are walking together and talking about Dr. Radcliffe, the tablet computer that Fitz' dad is holding jumps from his left hand to his right hand between shots.
The Return - S4-E21
Continuity mistake: During the fight between Coulson, May and the two Ivanovs, the metal pipe that Coulson is wielding gets bent when Ivanov takes it off him. When he throws the pipe to the floor, it's straight again.
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.