Episode #2.1 - S2-E1
Revealing mistake: Richard at home is reading a book on slavery. An English book, at least the cover and the big header of the first internal page are in English, and about slavery. But a quick peek before the cut easily reveals that the book is written in French and talks about cocktails. (00:28:10)
Episode #2.5 - S2-E5
Revealing mistake: When Ben Miller asks for the forensics report on the oyster and shot glass, the report has egregious spelling mistakes ("Specimin" instead of Specimen) and shows the victim testing positive for Oxycodone rather than strychnine! For the record, it is an entirely different lab test (a real one, with 'specimen' spelt correctly) done for a patient under prescription medications (morphine, oxycodone and benadryl) and its date is inconsistent with every other episode (it's a 03/19/2010 document and in the first season it was established the year was 2011), but these last details can be noticed only if you freeze-frame. (00:42:00)
Episode #2.7 - S2-E7
Revealing mistake: When we see the killer deal the fatal strike, the pipe misses a mile to the left. (00:48:00)
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.