Continuity mistake: The shots of Doran from his left rear shows him a couple feet away from the wall while frontal shots show him backed up against the wall.
Funeral at Fifty-Mile - S1-E22
Continuity mistake: When Jessica walks from the house to the barn at the end, she is wearing knee high brown boots. By the time she reaches the barn they have been replaced with court shoes.
Factual error: Calleigh Duquesne frequently wears completely inappropriate clothing throughout the whole series. She often wears blouses that are so low cut that the neckline is below the lower curve of her breasts. No officer of the court in the US would be allowed to dress this way. There is no grey area here, and this is not a character mistake - first time a CSI turned up at work dressed like that, she'd be sent home to change. Second time, she'd be on suspension until she agreed to change her dress standards. Also (and this regularly happens in CSI: NY as well) she is regularly wearing high heels - also a certain no-no for as CSI. Incidentally, male CSIs have equally strict dress standards.
Continuity mistake: When Jack speaks to Michael and Jin, as they build the raft, and then when he walks up the beach and inquires about Sawyer's trouble with his head, the backpack that Jack carries on his back is nylon, black/green with white trim. Yet, when Sawyer asks, "Sensitivity to light, that bad?" the backpack is suddenly transformed into solid black leather, of an entirely different style. Then, in following shots it jumps back and forth. (00:16:40)
Continuity mistake: Charlie, Olivia's former partner and friend in the FBI shows up in this episode during the interview with Mrs. Rusk, but Charlie was killed off by one of the shapeshifters in a previous episode, and the shapeshifter that killed Charlie was himself killed off by Olivia, who in other episodes reflected back on killing him. This episode was supposedly meant to be in season 1 as ep 21 or 22. Unknown why they didn't air it then, and decided to put it in the middle of season 2 (for no apparent reason).
Chapter One: The River's Edge - S1-E1
Revealing mistake: When Hermione opens the bag of money, one stack says "Motion Picture Use Only." (00:29:45)
Continuity mistake: At the end of the episode, the Mercedes S class that is burning is not the same car that Castle drove previously in the episode, it's an older model one. Either it's a mistake or has to do something with the plot resolution, decide yourselves...
They Have Been, They Are, They Will Be... - S1-E3
Continuity mistake: While Tony Vincenzo is eating, his butter knife instantly turns into a fork in the next shot.
The Crab with the Golden Claws: Part 2 - S1-E2
Other mistake: The newspaper article that features Tintin and Captain Haddock at the end of the episode is a flipped shot, as shown by the text that has been reversed. (00:43:35)
Continuity mistake: When Allison gives Kurt his breakfast muffin (in a brown paper bag), it suddenly jumps from his left hand to his right hand between shots.
Factual error: Sierra Nevada beer would not have been available in DC during this time period.
Revealing mistake: When the Capri crashes into the goal net & they go to arrest the suspect you can see sky satellite dishes on the houses in front of them. Satellite TV didn't start in the UK until the 80s.
Factual error: Raceme's girlfriend Morgan is seen in a mugshot taken by Edinburgh Police, Scotland. They are known as Lothian and Borders Police, not as shown "Lothan and Boarders". (00:28:30)
Continuity mistake: Scooby finds a clump of ape hair stuck in the wine cask. It cuts to the gang, then back to the cask as they walk up and suddenly the clump of hair is twice as thick. (00:16:45)
Continuity mistake: When Charlie Epps is writing a quadrillion on the whiteboard, the writing alternates between shots. Most noticably when he first writes it down, there is a significant downward tendency of the 000 groups. In the next shot, they are pretty much horizontal. Also the shapes of the commas alter.
Factual error: Kyle says he has to log on before school. The next shot shows "Monday 8 days later." 8 days before is a Sunday. (00:04:45)
Visible crew/equipment: At about 30 minutes into the episode, right after Cal says: "if Jeffrey knows about priox, he's going to jail. But I'm gonna be damn sure before I send him there", you can see a hand in the top right corner of the screen.
Factual error: In the whole episode, Romania is depicted as a monarchy with the king in a position that allows him to make political decisions. However, Romania ceased to be a monarchy in 1947. By the time depicted in the episode (circa 1997), Romania was a republic and its head of state was the president. Members of the ex-royal family did not hold any positions in the Romanian government and were certainly not authorized to represent Romania in international events.
Plot hole: The protagonist gets in the exclusive, multi-millionaire, invites-only auction because the invitation is on a printed letter that he faked. This means that the guards at the entrance don't have a guest list to check, and since nobody knows who this person is, the staff does run a background check on his identity when he makes the first outrageous bid...by looking his name up on Wikipedia. That's mighty low standards of security, especially for an auction that was supposed to be for a selected audience and the most important in France.