The Hustlers News of the Day - S3-E5
Factual error: They plant Albert's hair on a brush used by the Queen Mother in order to have a DNA sample taken from it match that taken from a hair plucked out of his head by Francis Owen, their mark. The Queen Mother's (non-existent) son would not have the same DNA as her. It could be used to establish a biological relationship but it would not be identical - it could not be. First, Albert's DNA is identifiable as that of a male. The lab testing the sample supposed to be the Queen Mother's would see that immediately. Second, a son's DNA is not identical to either of his parents or his siblings (if any) - it is at least 50% different. Any lab worth their fee would realise in a second that the two samples were from the same person. Another problem - Owen plucks the hair from Albert's head and Stacie handles the hair from Albert she plants on the hairbrush with bare fingers, in both cases hopelessly contaminating the samples with their DNA. The tests really are that sensitive.
The Hustlers News of the Day - S3-E5
Factual error: The laboratory technician uses a bog standard light microscope to match the two DNA samples, one from Albert and one allegedly from the Queen Mother. That's absurd. DNA samples are compared using a procedure known as SDS-PAGE, otherwise known as gel electrophoresis. This produces the familiar chart we know as DNA "fingerprints" - bands of light and dark showing the composition of a DNA sample which has been broken up by enzymes. You cannot examine DNA with a light microscope - you couldn't even do it with a scanning electron microscope.

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)
As One Flew Out of the Cuckoo's Nest, One Flew In - S4-E1
Character mistake: Near the end of the episode Danny refers to the money they have stolen, saying "Stacie is sitting next to half a million big ones." Anyone familiar with grifter slang knows a "big one" is a thousand dollars (or pounds, etc.) - certainly Danny Blue would know that. He just said that they have half a billion dollars in their hands. Not a mistake Danny Blue would make.

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)
Getting Even - S4-E3
Plot hole: At the end of the episode, having conned Veronica Powell out of £600,000 - the purchase price of the house and contents they sold her - Danny taunts her by telling her that they did nothing wrong, implying that she has no legal recourse to recovering her money. He's wrong. One of the gang, Billy Bond, bids against her in the auction for the house, boosting her bid from £220,000 to her final offer of £600,000. Bond has no money and no access to any, and no assets that could be realised to cover the bids he made, something that would be easy for a lawyer to prove. It's called shill bidding and it is very illegal indeed. Since Bond and Ash Morgan (who gave Powell false information during the auction, spurring her on to bid against Bond) are both standing next to Danny when he makes his announcement I find it hard to believe that a shrewd, hard-hearted businesswoman like her would not realise that she had been conned and would not get her lawyers and the police on the case on the spot.
Getting Even - S4-E3
Character mistake: Albert tells Ash that during his service in the UK with the U.S. Air Force he was required to join a squad flying back to the United States in a "B29 Fortress." The B29 Superfortress was not used in the European theatre during World War 2 - it was used exclusively in the war against Japan in the Pacific. The B17 Flying Fortress was a different aircraft. Anybody in the US Air Force at the time would know the difference, and it is not a mistake a veteran would make.

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)
Continuity mistake: In the dream sequence, Danny karate-kicks Shiro in the chest, knocking him backwards. You'd expect Shiro to land on his back if he's kicked in the chest and is falling backwards. However, in the next shot, he somehow lands on his stomach instead.
Factual error: The guys supposedly stole $5million. The largest US bill is $100. This means there would be 50,000 bills. $5million weighs 110lb. They would not have got that into a guitar case, far less Albert being able to carry it that easily.
Return of the Prodigal - S5-E1
Plot hole: Mickey Bricks returns to England by stealing the uniform of a Commander Cardwell, an officer in the Royal Navy, and taking his place on board an aircraft carrier that is sailing from Australia to the UK, leaving that day, a voyage that would take three to four weeks. During that time, Cardwell does not report his uniform stolen, nor does he report to the aircraft carrier to take up his duties, and since there was a car waiting to take him to the ship he is obviously supposed to be there. Theft of a military uniform is taken extremely seriously and once reported it would take no time at all to establish that "Cardwell" appears to be on board his ship! On top of that, during his entire time at sea nobody on board calls upon Mickey to perform any sort of military duties (of which he would have absolutely no knowledge), he doesn't run into anyone who knows Cardwell, and nobody asks to see his orders, military identification or travel warrant.
Return of the Prodigal - S5-E1
Factual error: There is absolutely no way prison visitors would be allowed into the cell of the prisoner they are visiting - they would not even be allowed into any part of the prison except for the visiting room. This is nothing to do with the guards going easy on Albert - they would be sacked on the spot for such a blatant and highly visible breach of prison rules.
Return of the Prodigal - S5-E1
Plot hole: Emma Kennedy gets into the morgue and coroner's office when she is wheeled in on a gurney sealed in a body bag. Mickey distracts the morgue attendant so she can get out of the bag and go to the coroner's filing room. All well and good, but what happens when the attendant goes back into the morgue after Mickey leaves and sees the empty body bag on the gurney? There is no indication that Emma gets back into the body bag and there is no reason for her to do so.

New Recruits - S5-E2
Other mistake: When Mickey first opens the newspaper to show the article on Fielding and Wood, in fact the article just repeats the same first three paragraphs of text again and again. (00:01:51)

New Recruits - S5-E2
Continuity mistake: When the gallery is initially shown, it is covered with red banners. When it is shown at the end of the episode, the banners have vanished. (00:45:17 - 00:57:15)
New Recruits - S5-E2
Factual error: The contract Stone and his team force Carlton Wood and Harry Fielding to sign guaranteeing Fowler's widow the royalties from his invention for life is signed under duress and is therefore invalid. It is hard to believe that none of Stone's team know this, but it is impossible to believe that Carlton Wood wouldn't.
New Recruits - S5-E2
Factual error: Knocking out fit, healthy adults by pumping an anaesthetic gas into a large, open room in which they are sitting is an incredibly stupid and dangerous thing to do. In order to do so, you'd have to know everything about them - age, weight, medical history, and so on. Killing them? Easy. Use cyanide gas. Knocking them out for a few hours? Impossible. Incidentally, why is it that the next morning when the grifters reveal their plan, nobody talks to the guards about what happened?
Other mistake: Mickey and Ash tell Sean and Emma all about the Fortnuss gold robbery, "the third largest bullion robbery in British criminal history." Emma tells them that they know absolutely nothing about it - they have never even heard of it. She goes on to explain that they don't know anything about the robbery because "We weren't exactly up on our current affairs in 1996." If neither she nor Sean knew anything about the raid, how would she know it took place in 1996? (00:06:29)
Factual error: As someone with a criminal record Mickey Bricks would not be allowed an "open" visit with Albert Stroller while he was in prison. Their visit would be "closed" - Stroller would be in a small booth, separated from Mickey by a Perspex screen.
Factual error: Emma gives their mark, Judge Anthony Stone, the name and address of Albert Stroller - Faverton Open Prison. Throughout the episode we see Stroller inside the prison, and we see what it looks like from outside when he is released. It is absolutely not an open prison, which would not have cell blocks and would not be enclosed in huge brick walls. The prison they show looks more like a medium or even high security inner city prison.
Suggested correction: There are a number of prisons in the UK that house both category C and D prisoners. This would mean it operates as an "open prison" to some prisoners, but still requires the security precautions of a higher security facility.
Rubbish. Stroller is under secure lockup - treated leniently by the guards perhaps but if the prison we see does have an 'open' section he most definitely is not in it.