This movie is an incredibly strange look into the mind (literally) of other people, which will of course provide many things to look at from a psychoanalytical perspective. There are a number of connections to the Hall reading for today throughout the movie. The idea of repressed childhood memories appears twice- once with Elijah the chimpanzee and once with John Malkovich. I thought Elijah's flashback scene was the most hilarious scene in the movie because of the ridiculous dialogue that is taking place. But this connects to the reading because of the psychoanalytical ideas presented in Hall, and how Elijah's memories were causing him trouble as an adult, and that to get better, he will have to "work through" it, like Lotte says. The second example of repressed memories is when the two girls are on the chase through John Malkovich's subconcious. All of the memories were embarassing and negative. I think it's very Freudian that the only memories shown in his subconcious were these memories, the types of memories that would cause someone problems in a psychoanalytical perspective.
Another connection I saw between the reading and the movie was Freud's idea that women were the "castrated" version of men. This can possibly be scene with Lotte, who feels so great when she is in John Malkovich that she decides she wants to be transgender. The fact that Lotte can only find sexual satisfaction as a man after her experience would fit into Freudian's psychoanalytical idea that women were inferior and, in some way, all longed to be men.
Overall, there is so much that can be analyzed in a movie as weird as this one, especially looking through the lens of psychoanalysis.