When Ripley uses Dickie's 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. This phrase was also used back in the day when people were learning how to use the typewriter... They learned the phrase then they had to keep repeating it to get their speed up. They are commonly used for analyzing a person's handwriting. In this case, it allowed Ripley to notice the "e" stamp was off center on Dickie's typewriter.
Jude Law, who played Dickie Greenleaf in Il talento di Mr. Ripley (1999), praised this series, "I'm enjoying it. How can one not? It's such great material. You're in great hands with wonderful actors, and it's such an interesting character. Both versions reflect the director in many ways. One is visual, colorful, and romantic. The other is quite forensic and more sinister. Film, to me, often reflects the person at the helm of the camera."
The Picasso painting in Dickie's home is "The Guitar Player", painted in 1910 during Picasso's Analytic Cubism phase. It resides at The Musée National d'Art Moderne, Centre Georges Pompidou in Paris.