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...
Audio problem: When they are trying to escape Koopa and the little caveman speaks, then Luigi answers him, he has the Princess' voice.
You Gotta Lose This Job - S3-E7
Visible crew/equipment: When 'Hannah' and Lilly walk into Rob Reiner's office, the multiple head studio lights are reflected on Hannah's large black sunglasses.
Revealing mistake: Any time any character is driving a Suburban, or any other vehicle with a column mounted shift lever, the shifter is in park while they appear to be driving.
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)
The Bridge - S1-E10
Revealing mistake: Agent Coulson turns the steering wheel several times despite the car being on a straight street.
Factual error: Bill wears four medal ribbons, in order: Diamond Jubilee Medal (awarded to all people with five years' service in a British uniformed service in 2012), Golden Jubilee Medal (the same in 2002), Queen's Police Medal (a very prestigious award, a handful of which are awarded every year to long-serving police officers for exceptional service) and Police Long Service and Good Conduct Medal (awarded for 20 years' unblemished service in the British police). Not only are these in the wrong order (it should be QPM, Golden Jubilee, Diamond Jubilee, LS&GCM), but he's not entitled to any of them! He's an American who hasn't previously served in the British police. A chief constable's uniform doesn't just come with medal ribbons for the look of it; only those that have been earned may be worn.
Character mistake: When Matt is talking to his priest Father Lantom, he says "it was a nice sermon" instead of "it was a nice homily." In the Catholic church "homily" is the correct word; sermons are Protestant. (00:11:30)
Do-It-Yourself Mr. Bean - S1-E13
Factual error: On a close-up of Mr. Bean's calendar at the very beginning, New Year's Eve 1993 is depicted as a Saturday, but in reality, this date fell on a Friday. (00:00:40)
Continuity mistake: Chase gives Zoey a radio in this episode, but in 1-3 Webcam, when Zoey, Quinn and Nicole are in Zoey's room trying to figure out who is telling the girls' secrets to people, you can see that radio above Zoey's head.
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.
Visible crew/equipment: When Topanga carries Cory into the room you can see a crew member's hand triggering the doors to open.
Continuity mistake: When Crockett tries to stop a rapist in a white Lamborghini the Lamborghini's taillights switches design during the chase.
Shrink It Up - S2-E1
Continuity mistake: When Rocky is saying things that she has been pushed into doing, she mentions the time they danced on the wings of a plane. However they didn't do that until a few episodes later.
Audio problem: When Michael is forced to do "errands" for Brennen, they stop by Jonathan Carver's house to get numbers from him for a voice key. The code played back at the facility is 71348. He says "3" in a medium pitch (tone) at the house, but it is high pitched when played back at the facility; he says "8" in a medium pitch, and it's also high pitched later. And finally he says "9" in a low pitch and it's played back medium pitch. Also very obvious is the fact that Jonathan never says "1" or "7."
Episode #1.8 - S1-E8
Factual error: When the bullion van leaves the yard a 1995 N reg Rover 600 is parked on the left hand side of the road, before Ray drives off in his Granada. In 1982 the Rover 600 was not even on the drawing board.
Gold Is Where You Leave It - S1-E19
Revealing mistake: Buck lights the fuse and tosses the dynamite-filled barrel at the bad guys. We see the explosion. Unfortunately, after that, we can also see the intact barrel still rolling away in the dirt.
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.
Putting a Hit on Christmas - S2-E7
Continuity mistake: The Christmas package in front of Kyle is fully but badly wrapped. When Eve turns back with new Christmas wrapping to re-wrap the package, it is fully unwrapped with not enough time for Kyle to remove the old wrapping.
Revealing mistake: Watch the opening sequence of this episode very carefully - Clarkson, May and Hammond are not in Downing Street (they are on a set that stands on the BBC backlot) and library footage of the Prime Minister is cleverly edited in to make it look as if they were there at the same time. Even taking into account the fact that the Prime Minister's security service would never allow such an intrusion onto Downing Street, the line up of the shots does not quite match - our three intrepid heroes should be visible in shot when the Prime Minister is shown exiting number 10, but they are nowhere to be seen. It is all sleight of hand and clever editing, but detectable if you watch carefully enough.