Deliberate mistake: The last season touched on Infinity War happening - this season jumps forwards a year, meaning that we should be one year into the "blip" (or snap), with half the universe missing. But The Team is all together, and the world/universe is utterly unaffected. Largely a byproduct of disagreement between the film and TV sides of Marvel, plus scheduling vagueness meaning they couldn't risk spoiling Endgame if they came back on the air before that was released. But considering the show is 100% part of the MCU, that's a pretty massive contradiction.
Other mistake: The module on the alien spacecraft Fitz repairs, most visible when he says "OK we're done, we're done" is just a standard PC motherboard, which also has no connections to anything else - it's just glued to the metal panel he's holding.
Collision Course (Part II) - S6-E9
Continuity mistake: When Mack and Davis slide down the rope, they're wearing gloves. You see Davis take his gloves off, but Mack hasn't quite started to when we see Yo-Yo close to landing. When the shot cuts, Yo-Yo is landing and Mack now has his gloves off as he draws his weapon.
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.