When the Right Hand Man connected Castle to the blue truth serum drip, he did not bleed the air out of the line so by the time the blue liquid actual hit his vein the air should already have finished him off.
The position of the DYE-2 radar station shown on the computer screen is far north of the Arctic Circle, not on it, as Vikram says. In fact, its position shows it on the North Pole ice cap. A fairly silly place to put it, as it, first of all, would drift with the pack ice, then, eventually, would have ended up at the bottom of the ocean, as the ice, after some years, would crack up and melt. A more logic place to have put it would have been the Thule Airbase on Greenland, still far north of the Arctic Circle.
Plastic guns are extremely unreliable and prone to bursting. On the other and, Titanium, while expensive is non-magnetic and every bit as sturdy as steel for firearms.
After having the truth serum Castle mentions Ryan and Esposito as people who know about LokSat. However, Castle does not know at that point that Vikram and Kate have told Ryan and Esposito about LokSat back at the precinct, therefore should not have mentioned them.
Castle was on the phone with Becket and she told him that she got Ryan and Esposito in the loop about LokSat, therefore Castle now knows about them knowing.
When Castle is talking to Loksat in the torture cell, the camera switches from Castle to LokSat three or four times. The blue liquid that is in the drip-feed varies as the framing changes. In the Castle's frame, it is 3/4 full. In Loksat's frame, it is half full.
When Mr Flynn sets fire to the car with Caleb in the boot he douses it in petrol (gasoline) which covers the bodywork as well as the trunk. When he sets it alight only the inside of the car burns. If he had actually used petrol as an accelerant then it would burn over the bodywork where it was splashed and would be more explosive as the vapour ignites. It burns more like a gel accelerant was used on the inside of the car only.
The car from the crime scene is traced by it having staggered wheels (wider wheels in the rear than the front). What was meant was the track width (the overall width between the outer edges of the wheels) would be wider in the rear than the front. Both are inaccurate as far as being exclusive to rear or mid engine cars, as many domestic and foreign front engine cars have wider rear track widths and also use wider rear wheels than front ones.