In this question, we're looking for where a misinterpretation occurs between the two characters, so let's walk through the conversation. Rose says to not see a certain movie based on "the worst review" she's read in years in the paper. Chester responds that he doesn't understand why that makes her not want to see the movie, and that in any case, nothing in the paper is well-written. Chester has interpreted Rose's comment here to mean that "the worst" modified the actual "review" itself, and so the review itself was "the worst" in terms of its quality. For example, the review was poorly written or off-base; thus, he follows up by saying that nothing in the paper is well-written, and is confused about what the quality of the writing has to do with Rose's willingness to see the movie. Rose, on the other hand, is saying that the review harshly criticizes the movie, to the point where it is one of the harshest reviews she's read in years. Thus, she is unwilling to watch the movie because the review portrays the movie in a bad light. Rose uses "worst" as a synonym for "harshest"; Chester interprets it as a synonym for "most poorly-written." Thus, the disagreement here is based on the understanding of "worst review."
We know it's not (C) because Rose brings up "the local paper," referring ostensibly to the local newspaper. Chester picks up on this, saying "nothing in that paper" (most likely the local newspaper as well) is well-written. Nothing with regards to "the local paper" suggests a misinterpretation. Hope this helps, and feel free to ask any further questions if anything is still confusing.