The following has SPOILERS, so go watch Fargo first!
What a pathetic man. Possibly the most pathetic character to ever grace the big screen. And most people don't understand why he is even in the movie.
Who is Mike Yanagita?
From what we can tell, he is an old friend of Marge's from high school.
Why is he so pathetic?
A few things throughout the scene characterize him as such:
1. Hugged Marge for an awkward amount of time.
2. Goes to sit next to Marge but is asked not to.
3. Tries to apologize.
4. "I always liked you so much!" followed by a creepy smile.
5. Practically starts to cry in front of Marge.
6. "You are such a super lady! I'm so lonely."
7. Lied about his wife dying to get sympathy from Marge.
What's the big deal about this scene?
Most people who see Fargo wonder why this scene was included. It doesn't seem to advance the plot in any way, so, therefore, doesn't have a purpose.
Is there a point to this scene?
There are two explanations. One is that when Marge learned that Mike had lied to her, it reminded her other people's ability to deceive. She thought back to her case and how she had just believed Jerry without any thought otherwise. Next thing you know, she goes back to Jerry and catches him in a lie. In this way, the Mike Yanagita scene did advance the plot. The other explanation is that the scene was created for the sole purpose of character development. Through Joel and Ethan Coen's brilliant writing, Marge's personality is further revealed. If you think like I do, then you might think that both of these explanation are too similar to be separated. The theory that I like the most and feel works the best is that this experience shows the viewer and Marge her personality in that she is too trusting. This helps characterize Marge and further illustrate the overall point of the movie (more on that in next question) to the viewer, and it gets Marge to reanalyze her past decisions in her case. So yes, there is a point to the scene.
What is the "overall point" of Fargo, and how does Marge's conversation with Mike further this point?
Fargo is about Marge's understanding of humanity. At first, she was slightly naive as to what people would do to get what they want. She lived in quiet Minnesota with her supportive husband, and even though she was a cop, she hadn't had experience with evil people. After finding the bodies near the beginning, she went along with the case as if it were an everyday case. Halfway through the movie, Mike and Marge had their talk. This was a pivotal scene because she started to understand how crooked some people could be. Then, at the end of the movie, she expressed her disbelief to Gaear (the guy who introduced Carl to the woodchipper) of how terrible the criminals were. Such violence and greed wouldn't have occurred to her. The last line of the movie sums it up:
Marge: "Well, I just don't understand it."
