Simon Pegg revealed that American actress Lake Bell stayed in character with her English accent during filming, even when not before the camera. It wasn't until photography was done and she thanked the assembled crew that they realized she wasn't English.
The story was based on screenwriter Tess Morris's real-life encounter at London Waterloo Station, where a man approached her and asked if she was his blind date. She wondered what would have happened if she had said yes.
Nancy and Jack argue over him hailing a taxi for "a ten-minute walk." Reminding her that she pretended to be a triathlete he dares her to run, swim, and cycle back to a bar where he's left his bag then they'll see who gets there first. Nancy starts off running, and wins the race by borrowing a bike, but for the stage in between she quite explicitly "swims" through a rowdy hen party that's blocking an alleyway.
In Rosita's, the song that Nancy tells Jack is their song is "Move Closer" by Phyllis Nelson. This is also the song that Sean sings to Nancy when they are in the toilet cubicle.