Both "see" and "watch" may be used, but the sentence potentially reads awkwardly, potentially seeming to be a mix-up of these quite different structures: 1) Titanic is such a good movie that everyone should watch/see it. 2) Titanic is a good movie that everyone should watch/see. While it is not impossible to use "such a good movie" just as an intensified form of "a good movie", when it is immediately followed by "that" the reader is led to expect that a "such ...
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