Christmas Special: Part 2 - S3-E2
Plot hole: Lee and Dawn overstay their tourist visa in the US, then fly back to the UK for the Office Christmas party. They then get into a taxi to go out to the airport in order to return to the US. They're kidding themselves. As I know (to my cost) when you overstay a tourist visa, the US Immigration Service finds out when you check in at the airport on departure. They'll be refused reentry, and probably barred from entering the US for up to six years. (I got a three year ban.) Neither Lee nor Dawn could possibly be unaware of this nor think they could beat the system as they would have been arrested when they checked in in Florida on departure (as I was), and they would have remained in small holding cells until the paperwork banning their return had been processed and their passports stamped 'Invalid for U.S. Entry', as mine was. (All this takes about seventy two hours, so they'd have missed the Christmas party anyway.) The mistake is NOT that they were able to leave the USA - that is explained (it's still not possible, but in the context of the show and the suspension of disbelief we are meant to believe it) the mistake is that they are on the way back to the airport to return. That's absurd. They would have been under no illusions as to their banned status re reentry to the USA.
Christmas Special: Part 2 - S3-E2
Revealing mistake: Many shots show the trees and bushes in full bloom despite the fact it's Christmas. Most notable is the tree outside the pub window in Brent's second date and the bushes outside Brent's window when he's driving around in the daytime. Acknowledged in the DVD commentary.
Answer: In the Christmas specials, David states the documentary crew stitched him up. In other words, he was made to look like an idiot by the way it was put together, but in actuality, he may not have been as bad as the documentary had made out. In addition, it's clear he let his upcoming celebrity status get to his head, something that would not have happened prior to the documentary crew's arrival. At the end of series 1, he mentioned one of his achievements was cutting expenditure without losing any staff.