Really interesting to see this discussion. I was having a discussion on this movie here and this is what I said there (slightly edited) in response to romeomike's comments on sadness:

Yes, yes, yes. Sadness is essential -- Joy (like R's parents) won't let Sadness touch the memories and be part of R's experience. Joy first starts to understand the importance of Sadness, when Sadness listens to the imaginary friend's feelings -- and helps the imaginary friend feel better.

The idea of sadness helping you feel better is shown when R finally expresses her feelings to her parents and they say that they feel sad too and miss Minnesota too. The hear her and she doesn't have to carry her sadness around by herself.

At the end we see Joy handing the core memories to Sadness and each memory changes colour somewhat. Each memory is tinged with sadness, as our memories are in life, because they are past. Joys and sorrows both. caeli says it well also -- emotions and memories become more complex and nuanced as we grow up. Empathy includes letting another person feel her feelings and work through them.