The car being driven by Castle while driving to his wedding was a Fifth Generation Mercedes S Class. But the car shown on fire is a Fourth Generation Mercedes S Class.
When Beckett and Castle are leaving the bar, the divorce papers are still on the counter.
As Castle drives from Manhattan to the Hamptons, he announces he is twenty minutes away; to his left can be seen hills a hundred feet high or more. There is no elevation like that anywhere near the Hamptons.
The computer tech mentions she was "scrubbing" the laptop to see what was on it. Scrubbing is a term used to delete data, not recover it.