The lights are on
Bad is a strong word. I'd say, poorly written. Mostly, it's the weird Voice acting that weighs it down... this is because Cage reused the French cast for the English dub and most weren't as good outside their native language.
Personally, I respect Heavy Rain far more as a technical and design accomplishment, than any kind of literary one.
But, if you want to see terrible writing... hoo boy, try David Cage's earlier game, Indigo Prohecy. Yes, Mr. Cage may be one of the worst writers ever.