When Chuck is fixing Orion's computer in Castle, he is using a black flexible roll-able keyboard with no switches, which makes no sound when used, yet you can hear the standard keyboard buttons clacking when Chuck and Ellie use it.
When they open the circular device holding Agent X's identity, several 3.5 inch floppy disks are revealed. Yet in 1980, when this device was sealed, 3.5 inch floppy disks did not exist yet. They weren't invented until 1982, with compatible drives coming out the following year. They weren't even the most popular floppy disk until 1988, when they replaced the 5.25 inch floppy. And on top of all of this, John Casey pops one in the computer, and it pops up with a nicely formatted display revealing Agent X's identity. Yet when the floppy disk would have been made, the data would have been saved only as plain text.
The vehicles that are parked outside the house in Somerset, England are left hand drive models. British vehicles are right hand drive. The vehicles are also not displaying VEL discs, which, before 1st October 2014, were mandatory for display in all vehicles.
During the shoot out scene, a US light switch is visible on the wall in the English house.
Chuck is claiming to be the first human Intersect even though he knows that Orion had a prototype Intersect downloaded in his brain before him.
When Chuck explains that their vehicle had broken down, the English lady invites him in to await "the lorry". There is no reason for them to be awaiting a lorry, which is a large truck. The correct term would be to 'await recovery'. In the UK, recovery may come in the form of a van or a recovery vehicle (similar to the US tow truck).
(at around 30 mins) Chuck asks Morgan for a katana (Japanese long sword); the sword Morgan picks out is clearly a short one (wakizashi).
At 35:09, when Mrs Winterbone stars shooting the machine gun, it's obvious that's not Millicent Martin who's doing it but a man with a wig.