It isn't clear what Lennie's unique mental challenges are, but he certainly interacts with others in ways that reflect an inability to reason in typically adult-like ways. Because of this, he has a great dependence on George and trusts that George will take care of him. This is one of the great ironies of the story; the man whom he trusts wholeheartedly is the man who actually kills him in the end.
Lennie loves to pet soft things, and he unfortunately doesn't realize his own strength. The animals die because Lennie pets them too roughly, and this demonstrates an inability to reason and respond appropriately to situations in his environment. Before they arrive at the ranch, George becomes suspicious that Lennie has hidden another animal from him and asks Lennie to produce it. Lennie insists that he found a dead mouse, and when George asks why he wants to carry around a dead mouse, Lennie responds,
I could pet it with my thumb while we walked along.
Lennie simply doesn't understand the harm in carrying around dead animals and is only concerned with the fact that they are soft and comforting. He cannot reason that they could carry diseases and could therefore cause him harm.
Later in this same scene, George gets angry with Lennie. Lennie seems quite childlike in his response:
If you don’t want me, you only jus’ got to say so, and I’ll go off in those hills right there—right up in those hills and live by myself. An’ I won’t get no mice stole from me.
Lennie basically threatens to run away, which is not feasible, because he isn't capable of taking care of himself. Unable to navigate the world of typical adults independently, he relies on George's sense of reasoning. Even more indicative of his childlike mindset in these lines is his focal point: In isolation, no one could take away his mice. He isn't concerned with surviving the elements or with feeding himself in the wild. His mind is only concerned with finally having the freedom to keep the pets he desperately longs for.
When Lennie talks to Curley's wife, she asks him why he's so "nuts" about rabbits. Again, his explanation reveals a childlike mind:
I like to pet nice things. Once at a fair I seen some of them long-hair rabbits. An' they was nice, you bet. Sometimes I've even pet mice, but not when I could get nothing better.
Lennie simply enjoys soft things. His explanation to Curley's wife doesn't reveal the rational mind of an experienced adult, who might comment on things such as rabbits' easygoing personalities, their bonds with their owners, or their ease in training. Instead, Lennie focuses on one tangible quality: softness.
Much of Lennie's dialogue and his responses to other adults around him reveal his mental challenges.