
Hard Times - S1-E3
Other mistake: Crowley shows acute discomfort while inside the church with Aziraphale and the Nazi spies as he is on consecrated ground. However, (spoiler alert) once the bomb destroys the church he is perfectly comfortable. The key word here is "ground" - it is the land upon which the church stands that is consecrated, not the building itself. (This allows churches to be rebuilt if they are demolished or destroyed.) Crowley should still be in considerable discomfort after the church has been blown up.

Factual error: When Klaus and Ben visit Dave at the hardware store in November 1963, they arrive in a 1965 Imperial. (00:32:48)

Character mistake: When Ginnifer Goodwin leaves the supermarket to go the parking garage, the green sign says 1 hour parking Customer's Only. It should say Customers Only, without the apostrophe.

A Single Piece Was Lost - S1-E10
Visible crew/equipment: When the Gruenaks attack the Scientist a puppeteer is visible to the right of one of the Gruenaks, just before it grabs the bird cage and throws it onto the Scientist's head. (00:28:18)

Continuity mistake: When Geralt fights the Striga, he ends up lying on his back with the Striga on top of him. To escape, he uses his magic to "punch" through the floor. The first attempt fails, its only effect is to blow away some dead leaves. At the second attempt a few seconds after, leaves are back on the floor.

Character mistake: When Harlan Edwards collapses and Dr. Arcane tells them to clear his airway, one of the other doctors addresses her as "Dr. Cane."

Character mistake: Shaun says that the underground facility is "built like a bunker", but the single missile they dodged just created a huge hole a moment earlier. (00:11:40)

Revealing mistake: Angelica and the other children are about to crash through the door to attack Lyra and Will. As Lyra runs past a cabinet, a lamp sitting on top is knocked over and crashes to the floor. Dafne Keene, who plays Lyra, reached over and very obviously pushed the lamp to the floor.

Welcome to Hotel del Luna - S1-E1
Continuity mistake: When the woman on the street greets younger Chan-sung, her right hand is raised slightly when she says "Tell me the year and hour that you were born", but in the next shot, her right hand is suddenly in her basket. (00:13:58)

Pride Parade - S5-E3
Factual error: Nandor manages to fly up to space, then loses control and falls back to earth in a fireball as he reenters the atmosphere. But objects reentering the atmosphere only get hot because they're generally travelling at immense speeds, 7-12 kilometers per second. Nandor just floated straight up, then falls straight back down. When Felix Baumgartner parachuted from the edge of space his maximum speed was about 1,300 km/h, and he didn't catch fire.

Revealing mistake: The ghosts often cast shadows.
Suggested correction: You can also hear their footsteps. But I'm not sure this is a mistake, just their own perception. Within the ghostly world they appear and act just like they would in life.
The ghosts are manifestations of energy, therefore they have no physical body to block light. Even if in the ghostly world, physics are physics and there should be no shadows.