Continuity mistake: When Taggart shoots the pile of skin grafts, it explodes, covering him, Jack, and Jo in guts. There's nothing on Tag's shoulder at first, but after a couple of shots, there is now a slab of skin on his right shoulder.
Other mistake: When Allison video calls Jack as he's finishing bathing, apparently she can see below the belt, as she remarks for him to cover himself up. But he gets dressed and doesn't move any reasonable distance from the screen, and we then see Allison's view which only captures Jack's torso, so she never would have seen his privates anyway.
Revealing mistake: When Carter and Jo talk to Fargo in the cage, the first clip has him floating in mid-air. Then, the force field expands. It cuts away, and when it goes back to Fargo, they didn't remove the rig he was sitting on to make him float in the first shot.
God Is in the Details - S2-E10
Character mistake: When Diane quotes the scripture, she says "Revelations." However, it's just "Revelation." Someone as smart as her who has read the New Testament (or heard it quoted) would know the correct word.
Continuity mistake: When the toilet at the Sheriff's Office explodes, it slides out into the main office, with no smoke coming from it. Two shots later, it is now emanating smoke.
Continuity mistake: We see that there's a "Do Not Cross" hologram in front of Cafe Diem when Henry arrives to check things out. When the group leaves, the hologram disappears from the outside shot.