Factual error: One of the songs played on the boat party is too early for july 1981. "Ay Ay Ay Ay Mosey" by Modern Romance was a Christmas time hit that year.

Plot hole: In episode 2, Alex Drake and the property developer Moore go to the Blitz club in Covent Garden, London. This club is well documented as having a very strict dress code with reports of people being turned away for very obscure reasons. Even "making an effort" wouldn't have been enough to gain entry. Everyone in the club, except Alex Drake and Moore, was "dressed up" in what came to be called "New Romantic" outfits, including two (off duty) members of Alex's team. It would've been impossible for Alex Drake or Moore to have entered the club wearing the "normal" clothes they had been wearing in the previous scene in the wine bar.