* The Score (2001): De Niro plays a professional thief planning a big heist, involving a producer's valuable necklace. The heist goes wrong, and the film explores the ensuing mysteries and betrayals.
* The Irishman (2019): While not a mystery in the traditional sense, this film features De Niro as a hitman who reflects on his life and the mysteries surrounding his past actions, including his involvement with Frank Sheeran, who worked with notorious figures in the entertainment industry.
* Analyze This (1999) & Analyze That (2002): De Niro plays a mob boss who seeks therapy from a psychiatrist. While not a mystery film, the therapy sessions involve uncovering past traumas and hidden motivations, which could be considered a form of personal mystery.
It's worth noting that Robert De Niro has a long and illustrious career, and there might be other films where he plays characters connected to the industry in some way. You could try searching for "Robert De Niro" and "film producer" to find more specific examples.
If you're looking for a film about a producer solving a mystery, you might enjoy "The Player" (1992), which features Tim Robbins as a Hollywood producer involved in a murder mystery.