I've seen the theatrical version and (I believe) the director's cut. The difference to me is pretty subtle - but I haven't studied it. Spoiler tag added for the poor souls who haven't seen this yet.
In the director's cut, which has the unicorn dream scene, it seems to me that the meaning of Gaff's origami is clearer - I believe they all apply to Deckard (chicken, man, and unicorn), and thus it shows that Gaff knows that Deckard is a replicant, because he has no way to know of Deckard's dream otherwise. Without the dream scene, the audience might believe the unicorn was meant to represent Rachel and her uniqueness.
You're missing the "eye thing", which not even Ridley Scott and Harrison Ford can agree upon. In fact, in the Theatrical Cut there's an error in the logic. Besides which, the scene you're talking about was lifted from Legend. Ridley denies this but it's totally legend. There's more to do with Ridley Scott saying "fuck you" to the studio than any sort of narrative brilliance.
Not sure what you mean by "eye thing". Related to the eye maker who leads them to Sebastion?
I was really just pointing out that the unicorn scene is (I believe) completely missing in the theatrical version, which sorta precludes any connection between that and Gaff's unicorn origami.
Okay. SPOILERS BELOW FOR BLADE RUNNER. . . . . . . . . . . . . . . . According to Ridley Scott, every replicant in Blade Runner has a "cat eye" flash upon light. google "owl blade runner" and know that every replicant in it - Pris, Rachel, Roy, the owl, Zhora, all of them, including Deckerd - show cat eyes at some point. However, there's a shot in the Final Cut where Deckerd most assuredly is not flashing a cat eye. It doesn't exactly cement things. The unicorn "scene" is missing in the theatrical version, but Gaff makes an origami Unicorn shortly before the voiceover talks about how "unique" Rachel is. Ridley cut some footage from Legend back into the film when he got to do his "director's Cut."