Felicity, Andy's assistant from the start of the film, is named after a young woman from Stockport, called Fliss, who tragically passed away. She was a massive Simon Pegg fan and he had sent her signed pictures at the request of her dad when she was ill. She passed before she could receive them. When Simon Pegg found out, he wrote the character into the movie in her memory.
The bartenders ("publicans") of the first two bars are, by complete coincidence, real-life cousins Teddy Kempner and Mark Kempner, who hadn't seen each other in years until they were reunited at the audition, according to director Edgar Wright.
When Sam joins the boys at The Old Familiar pub, everyone stands to greet her except for Gary. This alludes to their medieval names (King, Knight(ley), Page, Chamberlain, Prince) where everyone in the king's court would rise to greet a visitor, except for the king himself.
In every pub, the emblem of The Network (five vertical lines, longest in the middle) can be seen on the beer taps