Lennie, the not-so-gentle giant with the brain of a child, has several conflicts which have gotten him, as well as his friend and guardian George, in a lot of trouble.
Lennie versus his own nature:
The first problem is Lennie's own nature. Having been born cognitively decelerated, he is entirely dependent on those around him who have more tools and mechanisms to deal with an unforgiving society. In this case, it is George, a man with whom Lennie grew up, that has ended up taking care of Lennie.
While George is in some ways more fit than Lennie to deal with the world, Lennie is, by far, the strongest of the two. This is also a problem. Lennie does not realize exactly how strong he is. His emotional make up is immature and impulsive. Combined with unnatural strength, and an immense size, all of these factors become a recipe for disaster. And disaster it was: Unbeknownst to Lennie, he has killed animals, groped women, and now he will also kill Curley's wife in a moment of sexual arousal.
Lennie's strength leads him to other problems. He crushes Curley's hand (we don't really mind about that one) when the latter instigates him and punches him. He also breaks into people's personal space, and talks incessantly about things that others find foolish. These things render Lennie as an awkward individual to be with, and one who could be prone to verbal abuse from others.
Lennie versus human nature
Curley, a pitiful, catty, petty, and unmanly cretin likes to pick on the less likely to defend themselves. That is what he was thinking when he went to bother Lennie to try and pick on him. At the request of George, who was fed up with Curley, Lennie counterattacks, and this is where the hand-crushing incident occurs. The problem with this is that Curley is an evil, nasty man who will never forgive Lennie. As such, he will find a way to get back at him, even though Slim threatened him if he dared.
When Curley finds out that Lennie killed his wife, the chance for Curley's revenge comes all too swiftly. This is what causes George to do a mercy killing by shooting his friend, rather than by having him face the horrors of a lynch mob at the hands of the coward Curley.
Lennie versus the elements
As a man with mental impediments, Lennie does not recognize the clear signs of danger in nature. In section 1, George clearly tells Lennie not to drink water from a still pond...which Lennie does anyway. George tells him to be careful with the puppies, which Lennie cannot do because he is too brusque. George asks him to stay away from Curley's wife, which he also cannot because he has sexual impulses as adolescent as his brain, so women are too tempting for him. Also, he is unable to discern who and what is considered "dangerous" or not.
Lennie was a problem about to happen. He has had way too much history behind him that shows that, the older he gets, the more problematic he becomes.