It sounds like the writer believes that the movie makers were forced to make the movie ("necessary") a certain bad way ("silliness"). However, his overall opinion is that the movie is good, maybe even great ("moving"), and that he wants to make sure the reader understands that he thinks the movie is mostly good and only has a little bit of bad. He is afraid the reader will think that he thinks the movie is completely bad, and he wants to make it clear that that is not his opinion ("don't get me wrong", "see past").
As for the literal meaning of the sentence, it is being given as a command.
"See past the necessary silliness" means...
"You (the person that I'm talking to) need to SEE PAST the necessary silliness that the movie makers included in the movie."
"You (the person that I'm talking to) need to REALIZE that this movie has some bad (some silliness), but that the movie makers didn't have a choice about putting that into the movie (it was necessary)."
"You (the person that I'm talking to) need to BE OPEN MINDED about the fact that the movie makers were forced to include some bad parts."
Hope that answers your question. :D