Character mistake: While investigating the "robbery" at the art gallery, DS Rivet enters the sterile crime scene without wearing gloves. He not only picks up a vital piece of evidence - a discarded receipt - with bare hands, he allows the salesperson in the shop it came from to handle it, too. Not only has he hopelessly contaminated the crime scene, he has made an important physical artifact useless as evidence.
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)
Curiosity Caught the Kat - S8-E3
Factual error: (Spoiler alert) At the end of the episode DCI Wainwright arrests DI Fisk on a charge of "corruption." As a senior police officer she would know there is no such charge, and the word "corruption" is far too general a term to be used as a criminal charge anyway. Fisk would be charged with "Misconduct in public office contrary to section 1 (1) of the Criminal Law Act 1977."
Factual error: There is absolutely no way that the police officers sent to arrest Mickey and his team would be armed. In the UK, a police officer would only carry a gun if they had clear evidence that their target was armed, and even then, the Armed Response Squad would be called in. Mickey and his team are white collar criminals with no history of violence and have never been known to carry or use weapons. They'd be arrested by unarmed police, just like almost everyone else.
Factual error: During this episode, Detective Sergeant Terri Hodges wears two blouses: one red and one beige. They show too much cleavage for a female police officer. If she showed up for duty dressed like that, she'd be sent home to change or out to a shop to buy a less revealing top.
Other mistake: As we know, given the shenanigans surrounding the abortive raid on the Millennium Dome diamond exhibition in 2000, if the authorities suspected that there was to be an organised raid on the Star of Africa exhibit, it would have been replaced with a paste replica.
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?
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.
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.
Factual error: Albert Stroller goes before the parole board, is approved, and released on the same day. That is impossible. The parole board will meet, interview the prisoner, then take depositions from other interested parties. If they approve parole, they will then pass their recommendation on to the Home Office who will approve or decline it. All this takes three or four days at least, so there is no way for Stroller to be out on the street to meet the bent judge right away.
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.