When Ripley uses Dickies typewriter for the first time, he types " The quick brown fox jumps over the lazy dog." This is a pangram, a phrase that uses every letter in the alphabet. They are commonly used for analyzing a persons handwriting. In this case, it allowed Ripley to notice the "e" stamp was off center on Dickies typewriter.
The Picasso painting in Dickie's home is "The Guitar Player," painted in 1910 during Picasso's Analytic Cubism phase. It currently resides at The Musee National d'Art Moderne, Centre Georges Pompidou in Paris.
The setting of Dickie Greenleaf's (Johnny Flynn) villa was not filmed in Atrani as depicted, but on the Italian island of Capri, legendary for being the home of Emperor Tiberius during his retirement from Ancient Roman politics.