It was actually raining for the filming of the scene where Dex and Emma are holidaying on a French beach. The actors performed under a tarpaulin in their swimsuits.
Anne Hathaway was clandestinely given the script as director Lone Scherfig wasn't looking at any American actresses for the part of Emma. Hathaway flew to London for a meeting with Scherfig which she described as "the worst meeting of my life.. I was just inarticulate". However, on leaving the director, she handed her a list of songs that she felt represented how she would interpret the character. It was this list that landed her the part.
There were some conversations about why cast an American actress to play Dexter's English mother but Lone Scherfig really liked the sense of experience, worldliness and flirtatiousness that Patricia Clarkson brought to the part.
The Coronas hit, "The Rhythm of the Night", was first released in December in 1993. In the movie it appears in July 1993, 6 months prior to its first actual release.
The wide shot of London in 1994 pans across the Houses of Parliament and then you catch sight of parliamentary office building, Portcullis House but it wasn't built for another 7 years.
At 1:18:45, where they were supposed to be in 2003, we see a BMW X6 parked on the side of the road, which in 2007 was a concept model of the BMW company and was later released in 2009.