One specific scene that was portrayed quite differently by multiple versions was the scene where Hamlet kills Polonius and confronts his mother, Gertrude, for marrying his father's murderer. When I first read this scene, I did not assume that the interactions between Gertrude and Hamlet were incestuous in any way. I assumed that this was simply a rather tense conversation between mother and son. And my original vision of the scene was supported by several of the film versions we watched (Kenneth Branagh's version and Laurence Olivier's versions, for example).
Then, however, we viewed the film version starring Mel Gibson as Hamlet, and this version portrayed the scene in a completely different way, creating an incestuous relationship between Hamlet and Gertrude. This simple change in portrayal of one scene changed the vibe of both versions completely, forcing us to question all of the interactions between Hamlet and Gertrude throughout the play. It also makes us wonder which type of portrayal Shakespeare originally intended, whether he viewed the relationship between Gertrude and Hamlet as incestuous or not. It's fascinating how the change in portrayal of just one scene can change the way we view an entire play.