Continuity mistake: At the very beginning of the movie when Riley is born, the shot from behind shows the mother wearing the glasses. In the next shot the glasses disappear.
Continuity mistake: When the friendship island falls, we have a zoomed out shot that shows a clear path of pink ground leading to the three other islands on the edge of the cliff with none of the memory storage units. This path disappears once we leave that shot. It also shows Imagination land as being right behind the island, roughly where Joy is standing, but she's in the memory storage convolutions before and after the landscape shot. (00:36:54)
Other mistake: When Riley and her parents arrive at their new home in San Francisco, several pieces of mail are sticking out of the mail slot in the door. A letter carrier would not deliver mail to a vacant house, let alone not push it all the way through the slot.
Continuity mistake: During the scene near the end when Joy gives the core memories to Sadness, we see the scenes on the screen which are supposed to be Riley's core memories. The first 4 are correct: Friendship, Family, Goofball, and Hockey. The last scene is supposed to be the last core memory: Honesty, where she reveals a hammer that she broke a plate with. Instead, it is the ice skating scene which Joy used earlier in the movie to replace the nightmare. (00:19:05 - 01:21:18)
Answer: Sadness can change the memories because of Riley's current situation: she has left the home she loved to move to a new city. This makes her happy memories more susceptible to being changed to sad memories. As she remembers things that used to make her happy they now make her sad because she hasn't accepted her new house as home yet. Presumably under the right circumstances the other emotions could do the same thing, just not all the time.