Deliberate mistake: When Joey and Jonathan get in Joey's car at Metropolis (just before heading to the police station), the car has headrests. When they get to the police station, see Lance Gessler leaving and then follow him, the car no longer has headrests. Obviously removed so as not to obstruct the actors.
Episode #1.3 - S1-E3
Deliberate mistake: When the judge shoots himself, the revolver slides across the table, to fake his murder by someone else. But there is no mechanism in place that explains how he does this, making it appear as if he is able to accurately throw/slide the gun after shooting himself. In the original novel, he used a rubber band to achieve the effect, but he is not shown setting it up here.
Deliberate mistake: When Dominique is creating a Tinder profile for Fiona (an app Fiona admits she doesn't use), she manages to use Fiona's phone to take a picture of her, create a profile, and quickly get three matches, all within a span of 25 seconds. Downloading the app itself would take longer than 25 seconds, much less agreeing to its terms of service, and verifying the email or phone number associated with the account. (00:45:15 - 00:45:39)
Plane Death - S1-E14
Deliberate mistake: When the bartender shoots the shotgun at Landon, the windows blow out the wrong way. This was likely done for the actors' safety. Also note how Landon flinches a bit off beat from the explosion.
Deliberate mistake: In the restaurant after their daughter finishes talking to Niko, Erik turns the tablet device around and sets it on the table to talk to Niko. From his perspective, he is looking down at the screen. But in the other shots from Niko's perspective, where he is a life sized hologram, his figure is shown looking up and meeting her eyes. But from her perspective it should look like he's looking down at the table.
Deliberate mistake: Rick is talking to Joe in a maximum security facility through glass without a phone. It is impossible to hear through such glass. One would literally have to scream and still it would be difficult to hear. They should be on a two-way phone and those conversations are at times recorded, especially with high profile prisoners like murderers, mafiosi, terrorists. There's no way they would get away about discussing murder and revenge without an intercept. (00:14:00 - 00:15:00)
The Night of the Tottering Tontine - S2-E16
Deliberate mistake: The knife that has just killed one of the investors doesn't have a trace of blood on it. No one had time to clean it off. (00:20:00)
Episode #3.6 - S3-E6
Deliberate mistake: When Fidel pops behind Humphrey with the walking cane, in nonsensical fashion his cane switches hands in the brief moment when the camera moves from behind him to the front of Humph. It has to be deliberate since there is no cut, but Fidel is standing still both times, and Gary Carr must have done a sudden swap that has no reason. (00:28:20)
Deliberate mistake: David is shown to have an illegal weapon in his home even though gun control is quite strict in the U.K. Sadly, this is quite a common practice by returning war veterans who feel safer with a gun in the house, as they often suffer from PTSD, as David does.