
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."

Der Kampf gegen den Drachen - S1-E3
Plot hole: Shiryu states that the Dragon Cloth, which has been 'for eons' under the waterfall (let's just say it's an exaggeration) is harder than diamond and invulnerable to any attack. In the original manga and anime series, Pegasus uses a sudden dodge during a daring grapple to get Shiryu to strike his own shield with the glove of the armor, shattering both ("invincible sword meets invincible shield") and causing him to fight barechested. In this remake, this whole part does not happen, so when Seiya wins the fight with a heart punch like in the other versions, he does it when Shiryu has his heart still covered by the thick breastplate of the armor, making the whole "Shiryu's armor is impervious to any hit and much stronger than any other Cloth" plot point completely moot.
Suggested correction: It is only said that the "Dragon Shield" is unbreakable.
No, says much more than that. "That might be true for other armors, but the Dragon Armor is special. Nothing can get past my shield. It's unbeatable. The day my Cosmo forced the waters of the Lushan to flow upwards, it revealed the Dragon Armor. Battered for eons by the falling water, the Armor had grown harder and more radiant than a diamond. My Armor is the hardest substance known to man. No matter how fast or hard you strike, you've lost, Seiya." He parried the blow with the shield and so that deserves a special mention, but they keep mentioning the armor as having intrinsic properties, and he is wearing the armor when he is struck by Seiya, which guards his heart. In the original anime and the manga he was armorless after Seiya wrecked it, in here it's intact. It makes no sense, which is why I categorize it as a plot hole and not just as Character error: it's not that maybe he's wrong about the armor, it's the whole situation that now is flawed reprising the original with key differences.

Continuity mistake: When Will Parry visits his grandparents, the grandmother is sitting on the sofa next to Will's grandfather. The grandmother's position keeps changing from sitting right next to him to being further apart.

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.