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It was originally intended to show full-frontal nudity of Ethan, likely during the shower scene at the start of the game. This was cut from the final release of the game.
Contributed by Dazz
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There are three points during the game which display Madison with some degree of nudity -- a shower scene in her apartment, a stripping scene at the Blue Lagoon, and a potential sex scene with Ethan Mars. Only her breasts and buttocks are shown. There is also a glitch where she, occasionally, will accidentally load her naked model.
Contributed by tigerlily
In the "Covered Market" chapter, Norman Jayden's actor, Leon Ockenden, actually kicked over one of the motion capture cameras. This is only visible when failing to jump over some boxes in the chase scene.
Contributed by tigerlily
During the early stages of development, Ethan's blackouts were going to be dreams, including him swimming underwater, trying to save Shaun, and seeing John Shepperd. These dreams were removed because they did not contribute to progressing through the story.
Contributed by tigerlily
The soundtrack was recorded by a full orchestra at Abbey Road Studios in London.
Contributed by tigerlily
All four characters have different colored eyes: Scott has hazel, Ethan has blue, Norman has green, and Madison has brown.
Contributed by tigerlily
All playable characters display a physical or mental illness: Ethan's blackouts, PTSD and agoraphobia, Scott's asthma, Norman's addiction to Triptocaine and Madison's insomnia.
Contributed by tigerlily
In the Epilogue of Heavy Rain, if the player saves Shaun with Madison and Ethan alive, it will show the three of them starting a new life. When they enter their new apartment, Ethan says "A friend of a friend let me jump in line."

In a previous game made by David Cage, Indigo Prophecy, the main character lives in the apartment that they are moving in to, and it is implied that "the friend of a friend" is Lucas Kane, the protagonist in Indigo Prophecy.
Contributed by retrolinkx