Continuity mistake: "A Stranger in Time, Part 2": Darien's arrival in 1993, shown in part 1, is recapped in part 2. But the director appears to have chosen different takes for the recap. Much of the dialogue differs substantially, and Selma's explanation that he's materialized in the ladies' room is left out altogether.
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Plot hole: "Showdown": Darien's lost hat and jacket reappear without explanation after Kane finds him wandering in the desert. Also unexplained is how Kane conveniently happens to be leading an extra, unnecessary horse - unnecessary, at least, until he stumbles across the stranded Darien.
Plot hole: "Cool Hand Darien": In the swamp, Luther overpowers both guards and escapes. As they were both out cold and no one else was around, he could easily have taken the keys from them and unlocked his leg shackles. Instead, assumedly because it's more dramatic, he sneaks back into the prison compound to steal a sledgehammer and break the chain.
Continuity mistake: "Out For Blood": Parker disintegrates a crystal decanter and wine glasses with his laser weapon, then fires at several more things in the house. During this sequence, he zaps the same decanter and glasses, which seem to have re-integrated, over again.
Continuity mistake: "Lethal Weapons": Darien is holding a disintegrator rifle when he leaps over the electronic fence. It flies from his hands when he lands, skidding across the porch, but disappears from the background when he gets up. It reappears just in time for him to snatch it up and shoot Cole with it.
Deliberate mistake: "Treasure of the Ages": Darien delivers Mary's child during the hurricane. There's no time lapse in the scene, but somehow the kid emerges perfectly clean: no blood, no placenta - and no umbilical cord. Darien also neglects to wash his hands before reaching in to turn the breeched baby around. (Ewwwwww!)
Revealing mistake: "The Crash": Due to the use of both models and stock footage, what is supposed to be one airplane has three very different appearances. As the passengers board, we see the "real" plane. In the air, it's another plane altogether (stock footage). When it crashes (a model), it looks completely different yet again.
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Factual error: "Treasure of the Ages": Haskell finds a jeweled cross that's supposedly from a shipwreck hundreds of years old. Only the relic he pulls from the sand is spotless: not a barnacle, rust spot or touch of encrustation on it. After centuries at the bottom of the ocean? Wouldn't happen.
Continuity mistake: "Cool Hand Darien": When Luther breaks the chain on his shackles, he is still wearing the leg cuffs and the trailing pieces of chain on either side. He doesn't stop anywhere to come across a key, but when he bursts into the mine to rescue Darien, the shackles have disappeared.