The Mysterious Affair at Styles - S3-E1
Plot hole: Can't fault this massive plot hole to the adaptation, but to the source material; the culprit (forgetting the stupidity of writing an incriminating letter detailing the plan to murder someone, and put it in a desk he shares with her) since there are people outside the room that are about to enter, tears the letter in 3 neat vertical strips, rolls them, puts them in the vase on the mantlepiece, and then opens the side door to slip away...instead of simply pocketing the letter and going through that same door. Nobody was going to search him or anything and could have burned it, torn it into confetti, anything, later. It takes way way longer to do what he did, which needed him to stay there in the room increasing the chances of being found out. And of course he and his accomplice do not retrieve the letter after.
The Leap Home (1) - November 25, 1969 - S3-E1
Factual error: The Post Raisin Bran cereal box sitting on the Beckett family breakfast table in 1969 has a 1990s box design. (00:18:00)
Continuity mistake: When Red Buckley is about to enter Emil Duval's house at night before discovering the black pearl, the lights inside the house are on, but when he finally enters the house they are off. Later when he goes out, they are on again.