Ding Dong That's My Song - S8-E5
Character mistake: When footage of Dale's gameshow is shown, the announcer states that it is coming to viewers live on a Friday. However, Ash later states that the show was shown to viewers live every Saturday.
Factual error: The gadget Ash gets Shaun to hide inside the bank vault deposit box is essentially a large and extremely powerful electromagnet. An electromagnet powerful enough to support a grown woman's weight (which it does later in the episode, when Emma uses it) would require significant power: either from a mains supply of electricity (which isn't possible, given the device is locked inside a deposit box), or else from batteries far larger than what could fit inside the gadget as shown on screen.
The Henderson Challenge - S3-E2
Visible crew/equipment: As Danny (who is supposedly naked) gets into the taxi, you can see he's wearing some kind of flesh-coloured thong. (00:11:35)
Gold Finger - S8-E1
Continuity mistake: When talking to Sean, Ash says that Liverpool play like a "bunch of girls" (not realising Sean is recording him saying this). However, when Sean subsequently plays the tape, in the recording Ash now describes a team as playing like a "load of girls" instead.
Character mistake: The amount of money the team allegedly scammed the first mark for keeps changing throughout. In the first scene, it appears to be £25K (the mark gives them this as a bribe). However, in the next scene when the team divide the money up, it is stated to be £105K. However then, in the penultimate scene, when the mark thinks Mickey has given him "60-70K" (Ash's words) from their new horse racing con, he states that he has made a 50 grand profit: thus suggesting again he was scammed out of 25k.

Continuity mistake: The scene where Danny is lying on the sofa in the flat listening to music. Stacey throws down an envelope of money onto his chest. The banknotes spill considerably out of the envelope in the first shot. Two shots later and without either Danny or Stacey having touched the money, the banknotes are mysteriously tucked back inside the envelope.

Continuity mistake: Stacie is calling an ambulance, holding the phone in her right hand. In the following shot, the phone is in her left hand. (00:03:45)
Other mistake: The end credits for this episode are actually a repeat of the credits for the previous episode Lest Ye Be Judged. (00:51:10)

Continuity mistake: As Victor and Mickey are talking in Victor's office, Victor has his feet placed on his desk. He then removes them and leans forward to speak to Mickey. In the next shot, his feet are suddenly on the desk again. (00:11:50)

Continuity mistake: Shiro cuts Stacey's right cheek with his sword, drawing blood. However, in subsequent shots, Stacey's cheek is completely unmarked, and there is no sign of any cut or blood. (00:32:46 - 00:33:58)

Getting Even - S4-E3
Factual error: Ash gives Albert a slip of paper with Lily's home address, including a postcode of WC2E. That postcode is in Central London, but the house Albert then goes to is somewhere far more suburban, a long way from WC2. (00:50:21 - 00:55:22)

Continuity mistake: When Danny and Stacey walk into the Human Resources office, a shot of the woman behind the desk shows the glass countertop has nothing on it. However, when Stacey spins the monitor around, a mouse suddenly appears in the next shot on the glass countertop. (00:30:05)

Continuity mistake: When Mickey and Ash are sitting with Wendy in the restaurant, Mickey deliberately knocks over the jug of milk, causing a puddle of spilt milk. However, when the wide shot of the three characters is then shown, the jug is upright, and there is no puddle of spilt milk. (00:42:46)
Factual error: The police visit Richard Shaw's estate agency towards the end of the episode. The establishing background shot opposite where the estate agency allegedly is is of what was then the Cable and Wireless Building (long since bought by Vodafone). That building's real-life address is in the SE1 postcode. The problem is that the business card the police officer holds with the address has a completely different postcode.
Character mistake: When Mickey and Emma are trying to get access to the university labs, they claim they are working for Ofsted, and are investigating exam manipulation allegations. In fact, Ofsted have never been responsible for supervising/investigating universities - they only cover places of education up to the age of 18. Completely different organisations supervise universities.
Deliberate mistake: When Sam first meets Mickey (who is posing as a bank robber), Mickey says he needs Sam to state that he needs Mickey's help in robbing a bank, so if Sam turns out to be an undercover cop, Mickey can plead entrapment. This is a classic error. Entrapment only exists where a cop actively persuades a criminal to do something he otherwise wouldn't have done - which is not the case here. If Mickey as a con artist knows this (which is likely), it's a deliberate mistake, otherwise it's a factual error. (00:30:09)
Plot hole: When Albert, Mickey and Emma are trying to decide which nationality of millionaire Albert will pose as, they decide not to go with an English millionaire, since Albert at this point tries and fails to do a remotely convincing upper-class English accent. However, in many earlier episodes (such as "Gold Mine") he has no problems at all in putting on a convincing upper-class English accent.
Factual error: In the flashback scene to Whittaker senior's trial at the Old Bailey (which takes place in the late 19th or early 20th century), the judge in the trial is wearing a long, full-bottomed wig. This is completely incorrect - since the late 18th century, full-bottomed wigs have only been worn by judges on ceremonial occasions, not in court. At trials, judges wear short wigs instead. (00:05:17)