I wonder if it is beneficial to the site for us or the OP or whoever has the privilege to tag these questions with the movie that they were identified as?
No, this should absolutely not be done for various reasons (in order of importance):
- Tags are entirely about the question, not about topics tangential to the question or, as in this case, its answers alone. We are not supposed to adapt a question's tags to its answers. Those are for all intents and purposes identification questions asking for a movie, not questions about that movie itself.
- From a mere practical viewpoint, someone interested in questions about a specific movie doesn't care about all the ID questions asking for it, since he already knows that movie and the ID questions are already accepted anyway.
- Apart from the conceptual mistake this would be, it would also be an utter maintenance nightmare if you want to do it consistently (and god beware we do this in an inconsistent and fuzzy way). You would have to retag each and every identification question whenever an answer of it gets accepted and people already have difficulties with properly tagging questions on creation.
- It has never been done for the lifetime of this site (including the 2.5 years since this question was asked). This doesn't make it automatically unviable, but it suggests a certain degree of accepted "common law".