I would add that the idea of a man carrying a dead mouse in his pocket is rather disgusting. It seems intended to show that there is something wrong with Lennie mentally. It would be bad enough to carry a live mouse around, but to carry a dead mouse seems sick. That is probably why George takes the mouse away from Lennie. George is a little disgusted himself--although he must be used to these kinds of things from Lennie. How long does Lennie intend to keep the dead mouse in his pocket? Would he keep it even after it started to decay?
The incident with the dead mouse also reveals that he is becoming more resistant to obeying George and that he lies to him all the time. It also demonstrates that Lennie kills things he pets, either accidentally or intentionally.
"Come on. Give it to me. You ain't puttin' nothing over."
Lennie hesitated, backed away, looked wildly at the brush line as though he contemplated running for his freedom. George said coldly, "You gonna give me that mouse or do I have to sock you?"
Lennie is changing. He is beginning to realize that he doesn't have to do everything George tells him. He is thinking that he could live independently and then do whatever he wanted. He also reveals that he could become dangerous, not only to girls but to George himself.
"I'd pet 'em, and pretty soon they bit my fingers and I pinched their heads a little and then they was dead--because they was so little."
When George realizes that Lennie has killed Curley's wife in the barn in what looks very much like an attempted rape, he feels personally guilty. If he hadn't brought Lennie to that ranch and then talked the Boss into hiring him, the girl would still be alive. George also realizes that Lennie was probably lying to him about the incident in Weed. Lennie wasn't just trying to feel a girl's dress--which would be bad enough--but he was sexually attracted to her and might have tried to pull the dress off if George hadn't heard her screaming and come rushing back.
Carrying a dead mouse in his pocket shows that Lennie is an imbecile, a child. He isn't responsible for what he does because he doesn't have the mentality to understand himself or to control his own behavior. It is a mistake to feel too sympathetic for this character. He is potentially a menace because of his burgeoning sexual impulses, his weak mentality, and his enormous strength. The time could come when Lennie would stop submitting to being "socked" and verbally abused by George, and Lennie might kill his friend "accidentally."
It should be noted that rabbits are raised to be eaten. Lennie's fascination with rabbits is probably because he would get to pet them and also get to kill them.
The dead mouse reveals some distinct realities about Lennie. The first is the affinity Lennie has for "soft" things. He likes to pet the mouse because of how it feels. The mouse is dead. However, Lennie simply likes to pet it. Additionally, I think that the dead mouse shows his affinity for animals. From the dead mice to puppies to the elusive and idealistic way he glorifies rabbits, Lennie loves animals. His love for animals makes him child-like. His affection for the dead mouse reflects this part of his character. Finally, I think that the dead mouse in Lennie's jacket pocket shows the idea of how much he wishes for something to be his own. Like George, Lennie has dreams, as well. Lennie wishes for something he can call his own. Tending the rabbits, working on the farm, and having his own small place in the world are dreams he articulates throughout the narrative. To a large extent, these dreams begin with the dead mouse in his pocket that he pets and tends to—reflecting his desire for something he can call his own.